Having a Wyvern as a mount

[Ryuu Hayato]

What should I need to have a Wyvern as a mount? Mounted Combatant is a must have, but Animal Handling is really necessary? Can I use Persuation, like using on a Pegasus, to calm and trainning them?

[Lombra]

What should I need to have a Wyvern as a mount? Mounted Combatant is a must have, but Animal Handling is really necessary?

This is very DM dependant. Yes animal (even if it technically isn't an animal) handling would be fundamental, I'd even expertise it because if a Wyvern goes out of control it's way worse than a horse running around. Mounted combatant gives you a series of benefits that are the fundamentals of why you wanto to fight mounted.
Here's how our DM would do it: you have to find an egg of a wyvern (or a freshly hatched wyrmling) and look after it until the wyrmling comes out, then look after it until it becomes big and trained enaugh to be ridden in fight. It's not something that a low level character would be able to do, but I can see an high level character (11+) doing it.

[Ninja_Prawn]

but Animal Handling is really necessary? Can I use Persuation, like using on a Pegasus, to calm and trainning them?

I expect you'll find Animal Handling skills useful for raising and training a wyvern. I'd also ask for Animal Handling checks when riding in difficult circumstances or performing complex manoeuvres.

For me, you can't Persuade a wyvern. It doesn't speak a language and only has 5 Int... It's basically a very smart animal. A pegasus, on the other hand, understands 4 languages and has 10 Int, which puts it in a completely different league. You can't even use Speak with Animals to talk to a wyvern (in which case I might have allowed Persuasion), because it's not a beast - it's a dragon.

It might also be necessary to make some Arcana or Nature (depending on DM interpretation) checks to figure out how to raise a baby wyvern. I mean, that's not going to be common knowledge...