Is there Official Documentation Regarding Air Tank Transportation by Air

I checked with the airline about transporting the air tank, and they informed me that it may not be accepted either as carry-on baggage or checked baggage.

Since we may need to travel by air with this equipment for competitions, could you please provide any official documentation or certification stating that this air tank is permitted for air transportation?

Huh.

Airport screening let me through with an air tank in checked bags.

Make it clear the tank is NOT COMPRESSED and is empty.