Animation Module can make sagas skip either chapter 2 or 3, as I read it. Sagas trigger after draw step, so if you act prior to the next trigger, putting a 2nd counter on a saga would skip chapter 2 and adding a 3rd counter would cause it to be sacrificed.
It does not work that way. They have stated in the Dominaria Mechanics article that if you manage to add multiple counters to a saga, all of the corresponding chapters will trigger. AND you get to put them on the stack in any order.
So removing counters does not cause chapters to trigger
Not putting a counter on does not allow an existing chapter to trigger
Adding a single counter causes a single chapter to trigger (even if it has been triggered before; possible with counter removal)
Adding multiple counters causes all corresponding chapters to trigger (even if they have triggered before; possible with counter removal)
After the final chapter ability has left the stack (those are the rules words), the Saga is sacrificed as a state-based effect.