Driveability Problems

My son's 2000 s10 4.3 blazer has this problem. A rubber hose that is part of a pipe system that travels around the engine compartment is forced off the pipe. It comes from the exhaust manifold near the air box on the left side of the motor. The first time it came off it melted part of the air box. This seems to be part of the exhaust and emissions system but I am not sure.
Can anyone advise me what this is for.
Thanks for any advise

http://i142.photobucket.com/albums/r100/mrbizness1/blazerexaust.jpg

http://i142.photobucket.com/albums/r100/mrbizness1/hoseconnection.jpg

Looks much like the secondary AIR pump. Air injection reaction pump. I do not know the purpose of the thing.

On my '94 GM, it feeds into the intake, along with exhaust gasses in the crossover pipe (which is connected to both exhaust manifolds).

Dropped at dealer, the rubber hose (#16 in the diagram) started to burn up within a few miles of driving. Dealer says two of the air flow valves in that circuit are N/G. Repair cost will be about $375.00. Picking up tomorrow.

Picked up car today. Dealer replaced 2 check valves and the air pump that had water in it. valves were $78. pump was $354. total was $883.00 with tax,OUCH !!!! Check engine light is off.

thanks for the info cbec1999