user471: The Nanamoli and Bodhi translation of MN9 states in 2 excerpts:

With the arising of the taints there is the arising of ignorance. With
  the cessation of the taints there is the cessation of ignorance. .....
With the arising of ignorance there is the arising of the taints.
  With the cessation of ignorance there is the cessation of the taints.

The same 2 excerpts from the Thanissaro translation of MN9 reads:

From the origination of fermentation comes the origination of
  ignorance. From the cessation of fermentation comes the cessation of
  ignorance. .....
From the origination of ignorance comes the origination of
  fermentation. From the cessation of ignorance comes the cessation of
  fermentation.

When I took a look at the Pali version of Sammaditthi Sutta (MN9), I'm guessing that these phrases refer to:

Āsavasamudayā avijjāsamudayo, āsavanirodhā avijjānirodho .....
Avijjāsamudayā āsavasamudayo, avijjānirodhā āsavanirodho

How does this logic work?
When A arises, B arises. When A ceases, B ceases.
When B arises, A arises. When B ceases, A ceases.
Does this imply a cyclic causation (similar to chicken and egg)? Why is this the case? How does it work? How can the cycle be broken?

user254: Piya Tan writes that Bikkhu Ṇāṇananda wrote that it does involve a kind of cyclic:

79 Ṇāṇananda thinks that these two lines on ignorance and the influxes contradict the two in §66. In the former,
  he influxes” precedes “ignorance,” while in the latter, it is the reverse; but in the dependent arising, we see ignorance
  always appearing first (Ñāṇananda 2003: 104 f). We see here a reciprocal conditioning of the influxes (āsava)
  and of ignorance involves a kind of cycle, so that the influxes of ignorance (avijjâsava) is the condition for the arising
  of ignorance, and ignorance is the condition (avijjā) for the arising of influxes of ignorance. “The implication of
  this tendency could be to highlight the tendency of ignorance to perpetuate itself, the influx of ignorance [avijjâsava]
  representing the worldling’s habitual tendency to ignore the true nature of reality, a habit kept alive by its own
  effects, ignorant thought and action” (Analayo 2005 at M 1:54). Ñāṇavīra  notes: “avijjā…can have no anterior term
  that does not itself involve avijjā.” (1987:36)

Reading the original (i.e. page 104 onward of Nibbāna—the Mind Stilled), Bikkhu Ṇāṇananda says (my paraphrase) that the whole things is like watching a movie -- that ignorance is the dark theatre in/on which the movie is played, and the sankharas are the movie projected in the theatre; and with cessation of ignorance (light in the theatre) the sankharas no longer hold the spectator's attention.
Where the influxes come into that analogy seems to be that, in the original, it wasn't a movie but instead some kind of performance, a play or puppet show. So there are pauses in the production, while actors put on makeup, while the background is changed between scenes, and so on. It's due to the spectators influxes that the spectator enjoys watching the performance (perhaps, anticipating enjoyment) even during these pauses.

But if we are to understand the deeper implications of what the
  Buddha declared, with reference to the picture caraṇa, a film show
  or drama is produced, in the last analysis, by the spectator himself.
  When he goes to the cinema and the theatre, he takes with him the
  spices needed to concoct a film or a drama, and that is: the influxes,
  or āsavas. Whatever technical defects and shortcomings there are in
  them, he makes good with his influxes.
As we know, in a drama there is a certain interval between two
  scenes. But the average audience is able to appreciate even such a
  drama, because they are influenced by the influxes of sense desire,
  existence, and ignorance.

And

Now, for instance, let us think of an occasion when a film show is
  going on within the framework of darkness. In the case of a matinee
  show, doors and windows will have to be closed. Supposing the
  doors are suddenly flung open, while a vivid technicolour scene is
  flashing on the screen, what happens then? The spectators will find
  themselves suddenly thrown out of the cinema world they had created
  for themselves. Why? Because the scene in technicolour has
  now lost its colour. It has faded away. The result is dejection, disenchantment.
  The film show loses its significance.
That film show owed its existence to the dark framework of ignorance
  and the force of preparations. But now that the framework has
  broken down, such a vast change has come over, resulting in a disenchantment.
  Now the word rāga has a nuance suggestive of colour, so
  virāga, dispassion, can also literally mean a fading away or a decolouration.
  Here we have a possible instance of nibbidā virāga, disenchantment,
  dispassion, at least in a limited sense. 


user43: Yup, it's a vicious circle. On one side we have Ignorance/Confusion/Delusion and on the other Stress, Negative Emotions, and Bad Karma.
It is like being born in a poor uneducated family: because you are poor, you can't get education, and because you can't get education you are poor.
When you are stressed, you don't have time to stop and seek solution, you keep rolling day after day, never acting as per your plan, but only reacting to your issues. Because you keep rolling uncontrollably, very stressed, your head is not clear, your will is damaged, your perspective is skewed, so you keep sowing seeds for future trouble.
This is called "bewilderment", or as my teacher said:

One misstep begets another, begets another, and on, and on.

Imagine someone walking on a trail of rocks in the middle of a swamp, carrying a heavy backpack. Once you lose your balance and misstep off a rock, you're at a danger of falling in the swamp, so you have to compensate by making another sharp step sideways, but it does not end there - the inertia of the heavy backpack keeps carrying you on, so you have to keep making these sharp steps. You are lucky if you can stabilize yourself, but very often you end up running out of rocks and falling in the swamp.
The opposite of this, as often portrayed in suttas, is the good cycle of Sila/Samatha/Vipashyana. The more you fix your karma, the calmer you get, the more clearly you see, which allows you to further optimize your physical and mental action, which leads to even more peace, and even more clarity of vision and so on.

471: <p>The <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.009.ntbb.html#p66" rel="nofollow noreferrer">Nanamoli and Bodhi translation of MN9</a> states in 2 excerpts:</p>

<blockquote>
  <p>With the arising of the taints there is the arising of ignorance. With
  the cessation of the taints there is the cessation of ignorance. .....</p>
  
  <p>With the arising of ignorance there is the arising of the taints.
  With the cessation of ignorance there is the cessation of the taints.</p>
</blockquote>

<p>The same 2 excerpts from the <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.009.than.html" rel="nofollow noreferrer">Thanissaro translation of MN9</a> reads:</p>

<blockquote>
  <p>From the origination of fermentation comes the origination of
  ignorance. From the cessation of fermentation comes the cessation of
  ignorance. .....</p>
  
  <p>From the origination of ignorance comes the origination of
  fermentation. From the cessation of ignorance comes the cessation of
  fermentation.</p>
</blockquote>

<p>When I took a look at the <a href="https://suttacentral.net/mn9/pli/ms" rel="nofollow noreferrer">Pali version of Sammaditthi Sutta (MN9)</a>, I'm guessing that these phrases refer to:</p>

<blockquote>
  <p>Āsavasamudayā avijjāsamudayo, āsavanirodhā avijjānirodho .....</p>
  
  <p>Avijjāsamudayā āsavasamudayo, avijjānirodhā āsavanirodho</p>
</blockquote>

<p>How does this logic work?</p>

<p>When A arises, B arises. When A ceases, B ceases.</p>

<p>When B arises, A arises. When B ceases, A ceases.</p>

<p>Does this imply a cyclic causation (similar to chicken and egg)? Why is this the case? How does it work? How can the cycle be broken?</p>
 254: <p><a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/11.14-Samma-Ditthi-S-m9-piya.pdf" rel="nofollow noreferrer">Piya Tan writes</a> that Bikkhu Ṇāṇananda wrote that it does involve a kind of cyclic:</p>

<blockquote>
  <p><sup>79</sup> <strong>Ṇāṇananda</strong> thinks that these two lines on <em>ignorance and the influxes</em> contradict the two in <strong>§66</strong>. In the former,
  he influxes” precedes “ignorance,” while in the latter, it is the reverse; but in the dependent arising, we see <em>ignorance</em>
  always appearing first (Ñāṇananda 2003: 104 f). We see here a reciprocal conditioning of the influxes (<strong><em>āsava</em></strong>)
  and of ignorance involves a kind of cycle, so that the influxes of ignorance (<strong><em>avijjâsava</em></strong>) is the condition for the arising
  of ignorance, and ignorance is the condition (<em>avijjā</em>) for the arising of influxes of ignorance. “The implication of
  this tendency could be to highlight the tendency of ignorance to perpetuate itself, the influx of ignorance [<em>avijjâsava</em>]
  representing the worldling’s habitual tendency to ignore the true nature of reality, a habit kept alive by its own
  effects, ignorant thought and action” (<strong>Analayo</strong> 2005 at M 1:54). <strong>Ñāṇavīra</strong>  notes: “<em>avijjā</em>…can have no anterior term
  that does not itself involve <em>avijjā</em>.” (1987:36)</p>
</blockquote>

<p>Reading the original (i.e. page 104 onward of <em>Nibbāna—the Mind Stilled</em>), Bikkhu Ṇāṇananda says (my paraphrase) that the whole things is like watching a movie -- that ignorance is the dark theatre in/on which the movie is played, and the <em>sankharas</em> are the movie projected in the theatre; and with cessation of ignorance (light in the theatre) the <em>sankharas</em> no longer hold the spectator's attention.</p>

<p>Where the <em>influxes</em> come into that analogy seems to be that, in the original, it wasn't a movie but instead some kind of performance, a play or puppet show. So there are pauses in the production, while actors put on makeup, while the background is changed between scenes, and so on. It's due to the spectators influxes that the spectator enjoys watching the performance (perhaps, anticipating enjoyment) even during these pauses.</p>

<blockquote>
  <p>But if we are to understand the deeper implications of what the
  Buddha declared, with reference to the picture <em>caraṇa</em>, a film show
  or drama is produced, in the last analysis, by the spectator himself.
  When he goes to the cinema and the theatre, he takes with him the
  spices needed to concoct a film or a drama, and that is: the influxes,
  or <em>āsavas</em>. Whatever technical defects and shortcomings there are in
  them, he makes good with his influxes.</p>
  
  <p>As we know, in a drama there is a certain interval between two
  scenes. But the average audience is able to appreciate even such a
  drama, because they are influenced by the influxes of sense desire,
  existence, and ignorance.</p>
</blockquote>

<p>And</p>

<blockquote>
  <p>Now, for instance, let us think of an occasion when a film show is
  going on within the framework of darkness. In the case of a matinee
  show, doors and windows will have to be closed. Supposing the
  doors are suddenly flung open, while a vivid technicolour scene is
  flashing on the screen, what happens then? The spectators will find
  themselves suddenly thrown out of the cinema world they had created
  for themselves. Why? Because the scene in technicolour has
  now lost its colour. It has faded away. The result is dejection, disenchantment.
  The film show loses its significance.</p>
  
  <p>That film show owed its existence to the dark framework of ignorance
  and the force of preparations. But now that the framework has
  broken down, such a vast change has come over, resulting in a disenchantment.
  Now the word <em>rāga</em> has a nuance suggestive of colour, so
  <em>virāga</em>, dispassion, can also literally mean a fading away or a decolouration.
  Here we have a possible instance of <em>nibbidā virāga</em>, disenchantment,
  dispassion, at least in a limited sense. </p>
</blockquote>
 43: <p>Yup, it's a vicious circle. On one side we have Ignorance/Confusion/Delusion and on the other Stress, Negative Emotions, and Bad Karma.</p>

<p>It is like being born in a poor uneducated family: because you are poor, you can't get education, and because you can't get education you are poor.</p>

<p>When you are stressed, you don't have time to stop and seek solution, you keep rolling day after day, never acting as per your plan, but only <em>re</em>acting to your issues. Because you keep rolling uncontrollably, very stressed, your head is not clear, your will is damaged, your perspective is skewed, so you keep sowing seeds for future trouble.</p>

<p>This is called "bewilderment", or as my teacher said:</p>

<blockquote>
  <p>One misstep begets another, begets another, and on, and on.</p>
</blockquote>

<p>Imagine someone walking on a trail of rocks in the middle of a swamp, carrying a heavy backpack. Once you lose your balance and misstep off a rock, you're at a danger of falling in the swamp, so you have to compensate by making another sharp step sideways, but it does not end there - the inertia of the heavy backpack keeps carrying you on, so you have to keep making these sharp steps. You are lucky if you can stabilize yourself, but very often you end up running out of rocks and falling in the swamp.</p>

<p>The opposite of this, as often portrayed in suttas, is the good cycle of Sila/Samatha/Vipashyana. The more you fix your karma, the calmer you get, the more clearly you see, which allows you to further optimize your physical and mental action, which leads to even more peace, and even more clarity of vision and so on.</p>
