You have a couple of options.
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Use Streaming Levels. Your persistent level would be assigned your game mode etc. Your maps would be streaming levels, and since you never unload the persistent level, your character will carry over.
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So before changing level, save your health to a variable inside your game instance. Upon loading a level, you get that health variable in the game instance and update your players health with it.
This guy explains the game instance well.
