The phrase "to manage the transition" means to handle or control the process of moving from one state or condition to another smoothly and efficiently. Full definition
I took your advice on how to manage the transition in such a way that would be best for my daughter, along with your advice on how best to communicate with her. (peterhaiman.com)
Begin by giving yourself time to accept the change, to adjust and understand that there will be a period of managing this transition. (social.hays.com)
But I wish there was a better way to manage the transition from print to digital with the newspapers. (housegoeshome.com)