what is this air hose?

The one circled in red is the same as the one highlighted in blue on the other side of the picture. They are valve cover relief vacuum hoses.

For the one circled in red, the intake tube provides suction (via the plenum & throttle body) to this hose and the blow-by gasses and oils from the valves are sucked out and burned in the cylinders. On the other side (blue highlight) the exact same function is performed, except the suction is coming from the lower plenum rather than the intake tube.

Bonus material: Anybody who does the "oil catch" mod should be tapping into both these lines, filtering the air before it is returned to the plenum.

You can leave them exactly as they are - all intakes account for this line and it usually just takes a hose clamp.
 
The one circled in red is a breather, the one highlighted in blue is the pcv valve to the plenum. The red one is not a vacuum line since the pcv valve can only flow one way. If you plug the hole on the breather hose, the plenum would not be able to suck the air out of the heads through the pcv... it is a one way system.
 
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