Venting two baths and oven range through common exhaust
I'm about to install exhaust venting for a rehab. The showers for the two bathrooms share a common wall between them, and the entry to the attic for the range exhaust will be about 5 feet from the showers. Both are at the end of the house and I was considering the possibility of venting all three through a common exhaust vent going through the sidewall.
Would I need some sort of equivalent of a plumbing check valve to prevent one fixture from blowing back into another room? Would wye connections be sufficient to direct the airflow?
If all vents start at 4 inches, would I need to increase the diameter of the common section that goes out through the sidewall to accommodate the case where all three might be running at the same time?
Thanks in advance!