Air admittance valve on sewage pump?

I am installing a BURCAM EASY FLUSH sewage pump system that I purchased from Home Depot. I am installing it in the basement of a ranch house built in 1963. My question is on venting the unit and the shower and sink in the new bathroom I am putting in.. The BURCAM system calls for a 3" vent. It would be very difficult to run a new 3" vent up through the floor and existing walls of the house allthough I will if I have to. I just found out about Air Admittance Valves. Could I use an air admittance valve to vent my system instead of running a new 3" line.Or can you run a vent line up the outside of a house (it would not look very nice though)
The Air Admittance Valve idea sounds really good, but I don't know all the applications they are valid for.

Aav

Sorry, but it will not work. It would create a "closed" sytem and since air could not escape, nothing would drain properly. You need at least a 2" vent for the system.

Thanks, and some more questions

Well I would rather run a 2" pipe then a 3" pipe. I didn't know if I could size the pipe down that way or not since it has a 3" hole for the vent pipe.
Should I run 3" pipe until I get to the ceiling of the basement and then reduce it to 2" to go through the floor and first floor walls and into theattic? And can I tee it into the existing 2" vent line that goes through the roof?

air admittance valve

I put in same system and the air admittance valve did not work. So I ran a 2 inch pvc line from the 3 inch to the roof not easy. I ran the line along basement wall until I got to an inside corner of a bed room ran it up the corner of the wall to the attic and them boxed it in with a stain oar looks great no noise