Put everything in your checked bag separately, like batteries in one battery-safe container, tanks in another container, juice in another, mod in another etc, so in case they are sketched out by one or the other, it's less likely they take all of it and might just take one container. Expect to loose it all and just take bare essentials. I'd get a smoktech groove V2 for like $50 or a $10 ego VV instead of possibly losing provaris.
I actually vaped right in my seat on jet blue and held it in so no vapor came out. They let me take a smoktech groove with a full kanger protank carry on, but they wouldn't let me carry on a belt sander. It says No Motorized Tools (such as chainsaws and generators, even if they are brand new), but they previously let me take a smoothie blender in my carry on with an engine stronger than the belt sander, so I didn't think much of the sander. I think they just don't like tools like wrenches and screwdrivers that can be used to take the plane apart. I packed the blender blades in my checked bag but they said I could have carried them on but wouldn't let me take the belt sander even if I cut the cord since there wasn't time to bring it to my checked luggage. Even if you call you airline and they okay it, it depends on the TSA/customs agent you pass by.