Say I have a creature with Persist and I give it Undying until end of turn. Later this turn, it is put into the graveyard, and I choose for the Persist ability to resolve before the Undying ability. Persist resolves, returning my creature from the graveyard to the battlefield with a -1/-1 counter on it.
At this point, I can think of three different things that might happen:
Undying returns it to the battlefield with a +1/+1 and a -1/-1, which then cancel out.
Undying never resolves because the creature can't be returned to the battlefield if it's already there, so it just keeps the -1/-1.
Undying returns it to the battlefield as if it was just summoned with no counters on it, and then puts a +1/+1 counter on it.
I would assume that the second ability would 'fizzle' as explained in this question because the creature is not longer in the graveyard, making #2 correct, but I'm not completely sure. Could someone explain what happens after my poor death-resistant-battlefield-loving creature is put into the graveyard?
Undying: When this creature dies, if it had no +1/+1 counters on it, return it to the battlefield under its owner's control with a +1/+1 counter on it.
Persist: When this creature dies, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it.