@ring There are multiple approaches to network synchronization, depending on the animation complexity and type of game you're developing.
In general you would need to let your game state dictate which animations are started on which track. If you get by with just synchronizing game state of your characters, and after game state synchronization implicitly apply the respective animations, that would likely be the simplest solution.
If that's not possible for whatever reason and you need to synchronize animations directly, you would need to add special synchronization components to your characters which check the AnimationState of your SkeletonAnimation component, serialize the required TrackEntry objects at all Tracks and then de-serialize them on the other end. Theoretically you could also modify the spine-csharp and spine-unity runtimes and augment it with Mirror plugin functionality, but I would recommend against that, as runtime updates will cause conflicts.
There is a related forum thread on a replay system here, which might be helpful:
https://esotericsoftware.com/forum/d/16713-replay-system-replaying-animation-manually/8