Taking an airbag with gas cartridge and activation handle on flights:
According to the regulations of the International Air Transport Association (IATA), you can take an avalanche airbag with cartridge and activator on flights:
"Avalanche rescue backpack, one (1) per person, containing a cylinder of compressed gas in Div. 2.2. May also be equipped with a pyrotechnic trigger mechanism containing less than 200 mg net of Div. 1.4S. The backpack must be packed in such a manner that it cannot be accidentally activated. The airbags within the backpacks must be fitted with pressure relief valves.“
N.B. Airlines can have own more specific regulations. Contact your airline before your trip, and ask them for a written content which allows you to take the airbag with you, preferably in English considering your flight back.
Keep the airbag, the activation handle and the cartridge in the same place (handle detached). On the websites of the manufacturers, you can usually find specific, official information forms on cartridges, handles, and airbags. Print them and take them with you.
Mammut forms: https://www.mammut.com/service/avalanche-airbags/user-manuals/
USA: Empty cartridges only!