Q:

constructing mechanical chase

I'm thinking about putting a mechanical chase in my home to connect the roof to the garage.  The chase would contain the flue for water heater and furnace, and possibly a dryer vent (separate from flue).  I'd also like a conduit for communication cables (satellite, internet, etc).  I don't know if there are codes I need to be aware of, and this type of thing is hard to search for on Yelp.   
[EDIT] I'm defining "chase" as a type of chimney or shaft.  Honestly, I don't know that I'm using the word correctly.  My water heater and furnace are in the garage, which sits underneath the main living area.  Both appliances are gas and they share a flue which goes from the garage (think basement), up through the main living area (in a closet surrounded by drywall - no access), and out the top of the flat roof.  I would like to move this about 3' so that I can make the corridor/chimney/shaft/chase bigger, and add a dryer vent and some conduit for cables.
Would any general contractor be able to do this, or should I look for specific labor?
Is this something I could DIY?

A:

Ok now we know the want is for the chase to be a verticle space with 2 or more vents and some electrical. Yes this can be done, enclosed vents are required to be triple walled pipe in my state and the wiring must be rated for the temp in that area. Many wire types are rated for 90deg C this is very hot and with some venting in the chase it will stay well below this threshold. The dryer vent may need a booster fan and can be single wall, I always suggest a booster when going verticle or more than ~15' horizontal.

