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Before you travel, make a few copies of the first sheet of the AP and keep them with you (along with the AP, of course)
When you are leaving the country, nobody asks for your AP
When you are coming back, the airline people at the other end will ask to see your visa. Calmly explain to them
that you have an "Parole Visa", and show them the AP (all 3 sheets). Then, offer to give them 1 of the copies you made.
Everywhere that you are asked, offer them a copy.
When you are entering the US, in the white form (which you have to fill before the plane lands), leave the
type of visa blank (and other "visa" related details blank too)
At the immigration area, get in line with the other visa holders (H1, F1, B1, etc.).
The INS officer will look at your AP and passport, and then send you (or take you) to a separate holding area, where
they will process your case. They will then take 1 of the 3 sheets, and give back the other two (with some stamp) to you.