Q:

"Transition to" vs. "transition into"

What is the correct phrasing:

transition into

vs

transition to 

Can you explain why? 
Here’s the context:

In partnering with us, businesses can transition to/into a digital publication etc.

A:

I feel "transition into" implies more significance to the occurrence. "Transition to" might be be a lesser or perhaps more common change. 
Like the difference between the act of adapting to a given circumstance and the act of changing one's nature.

She managed the transition to public school quite well.
The caterpillar will make the transition into a butterfly.

A:

Since I'm old hat, I suggest that 'transition' is not yet a verb and so, neither example is grammatically correct.

