It's really straight forward. Just follow the guidelines of the airline you are using. If it is an American based airline, almost all of them just ask you to fill out a REd card at the check in counter which is a "Firearms Declaration" Just scratch through the word firearm and right air rifle.
In terms of inspection, it depends on the knucklehead who is at the counter. However, most of the time they just ask you to open the case and put the red card in. They may ask you to show them it is unloaded. I haven't had anyone ever ask me to show them there was no pressure in the cylinder, although they have the right to. I believe it's because they don't understand a PCP.
Paul Plauche from the USA