The phrase "to survive the transition" means to successfully make it through a change or period of adjustment without any major negative effects. Full definition
Hopefully it can survive the transition from the page to the screen. (filmjunk.com)
Thankfully, the objective paragraph didn't survive the transition to shorter, more concise resumes. (theundercoverrecruiter.com)
I've survived a transition in publishing (I think, I hope) and am moving on to more books as well as doing more bakery and restaurant consulting. (betterbaking.com)