Well if you fly to Italy, things vary by airport. Flying into Austria, the shotgun was on the carousel. leaving was more exciting than entering and the same with Hungary. Cyprus, I had to help a bunch of Americans and the customs fill the forms. Portugal was getting the permit beforehand and signing in with the shotgun that was at special handling. Leaving was more complicated with a custom agent and police officer verifying all the paperwork in 5 copies with the airline signing off with a copy, the x-ray scanner signing off with a copy and even the baggage handler having to sign off with a copy. The easiest is flying into France and picking up your shotgun on a carousel and then driving where ever you want in the EC with no paperwork! .!!! Air France and KLM requires two weeks notice and your boarding pass has weap on it. Air Canada, one advises on check in (btw they charge $50 for the firearm and $50 for extra baggage each way!). You have weap on your boarding pass. With Air France and KLM, I get priority boarding and rarely on Air Canada. They think that you are an air marshal! . My worst experience was in Morocco where they left the unattended shotgun outside the terminal. I got a Moroccan custom official to look for it with me behind the terminal building!
BTW, if you find your shotgun on a carousel in Italy, go to the Polizia. They will fill out a "declarazionne" and fine the baggage company 600E. Otherwise on your way back, they will not have your shotgun in the system which will delay you for a few hours!
Henry