If you are planning to travel and want to fly with the bike I think it would be good to call the airline you would like to fly and start there, I would think that all airlines are different. Ryanair states clearly on their website that electric bikes cannot be transported. On Southwest you can ship the bike but perhaps not the battery unless it meets the requirements.
I have and actually carried an E-bike to India from Washington DC.
Qatar airlines was really friendly. One sporting equipment is allowed free of cost.
You could keep the batteries in your carry-on baggage as long as it's less than 100Whrs. If you're lucky, they will let you carry more and they may not question you.
Even though I had put lots of foam, padding, the rear wheel axle was poking out of the box. You could buy Aircaddy ( pretty good cardboard box) or use your own.