Fresh air idea for new pelpro. Advice? my idea pic included in post

[llidisky]

So i have a new pelpro pp130 im installing this weekend. I am running the vent pipe through my existing fireplace flu. Question is can I run a pvc fresh air intake tube up the flue as well? I thought about using pvc going into the back of the stove connected with a rubber coupling, I think the fresh air return is around 2". then at the first 90 elbow putting a 2" to 3" reducer and running 3" pvc the rest of way up the flu and once i get to the top rain guard, cutting a hole and putting two 90's so it is facing down and away from the exhaust. the diagram is what i was thinking and it is a ms paint drawing so i know it is basic but hopefully will drive my question home better. if pvc wouldn't be best choice i could use gas

 

[heat seeker]

Any piping near the stove should be fire resistant! There are occasions where fire/heat can flow out the intake, and plastic piping couldn't take the heat, may cause a fire in the house.