I think your simplification is wrong. I computed BDDs for the original formula and yours and these are different. From the BDD of the original formula, you can get the transitions you are interested in.

Bytheway, a minimal DNF of the transition relation is

- !p&!q&o&!next(q) | !p&!a&o&!next(q) | !p&o&!next(p)&!next(q)