Transportation of bikes

I haven't had to transport bikes yet and I found it pretty difficult. Each airline and country has its own rules and they change frequently

I can't comment on the specific route you've indicated, but have transported my bike from the US (St. Louis) to Cairo, Egypt. It was actually way easier than I thought it was going to be. I flew Delta. I bought a hard sided case, because I don't trust airlines. I arrived early to ensure there was plenty of time to check in before my flight. The biggest hassle of the whole thing was actually finding a taxi large enough to carry the bike box at the other end in Cairo.

One tip: if you are running tubeless tires, do not deflate them much (airlines require some). You'll end up with sealant all over the inside of your bag, tire beads out of the rim, and likely no capacity to reinflate them with the pressure necessary to create a good seal.

I'm flying on Delta and they allow bikes!

Can't you take a train?