Introductions

So I want to come up with a plan to introduce all my females to each other. I have two new young females that are sisters whom I will be introducing to my three mature females (momma and two sisters). I have ordered a new cage that will be here next week and can hold up to six rats. The two young ones have four week old babies that they are housed with, they each had a litter. (pregnant when I got them, btw) I am re-homing the babies. My concern is how to most easily transition the moms from the birthing tanks to the new cage. The babies are eating/drinking on their own, but they still nurse occasionally. I've been looking online, so I have a good idea of what steps I should take, but I can't find much about specifically transitioning mommas. Will their behavior be any different? Should I be taking any special steps?