How would persist and undying work?
Persist is for -1/-1.
Undying is for +1/+1.
Do they cancel each other out?
Any time SBAs are checked and a +1/+1 countries on the same creature as a -1/-1 counter, both counters are removed.
So if a creature with Undying and Persist dies, it comes back with both counters, but the next time anyone gets priority the counters are removed.
Correct me if I'm wrong, but is it possible for BOTH abilities to bring the same card back? Wouldn't 1 ability trigger before the other, bringing it back with either a +1/+1 or -1/-1 respectively, then each additional time the creature would die it would be brought back by the opposite ability due to already having a +1/+1 or -1/-1 respectively?
...
Duh.
Sorry, migraine meds. Yes, only one resolves so you can alternate them and always bring the creature back.