Building Code question (HVAC)

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Trying to figure the best way to run the exhaust line (stale air) from the main floor ceiling back to the HRV in the basement and the only easy route in to use the HWT vent chase.

Wondering if okay to use the chase for the HRV duct. The duct be metal within the chase and this line vents to the outside of the house when the HRV is running.