Q:

How can I escape Bloodseeker's Rupture?

I would like to ask this question as I've been suffering quite badly from Bloodseeker's ultimate, Rupture recently.
So I would like to ask, what is considered "movement" in Dota 2? So far, I know that Phoenix's Icarus Dive is considered movement and would take rupture damage.
Another follow up question is, how do you escape without triggering the rupture damage from bloodseeker?

A:

Anything that makes your hero move from its previous location is concidered as a movement. e.g.  A secondary target to Beastmaster's Roar is pushed back and this is concidered a movement that would induce a HP loss from Rupture. (Here's a list of skills that force another hero to move (even very slightly))
In order to not take damage you basically have to break the 1300 distance limit in 0.25sec (or less). That means that technically moving at 5201+ movespeed would allow you to take no Rupture Damage while running. 
Getting a full list of what would allow you to escape Rupture damage is not really interesting and woud likely change overtime. However you can safely assume that any form of Global TP (Wisp, Furion, Kepper of the Light's Recall, Town Portal Scroll etc.) is ok to use. It is otherwise very hard to break that limit of 1300 distance per 0.25sec. 
Some exceptions to that are :

Queen of Pain which has a blink with 1300 range => by blinking and moving right away you won't take Rupture Damage. That's the only blink in the game with enough range to achieve that trick.
Clockwerk with HookShot level 3 (6000ms)
Storm's Ball Lightning (which makes him invulnerable)
Ember Spririt can join a remnnant (invulnerable while joining)
Puck can Orb out (since the Orb has a max range of 1800 and is joined instantly).

You can take a quick look at How to break the 522ms barrier in Dota 2.

