With regard to using ERV/HRVs for makeup air, we discussed this topic at length a couple years ago:
Using ERV/HRVs for Range Hood Makeup Air
A typical ERV/HRV is a balanced system (i.e., brings in the same amount of air as it exhausts) and has a much lower flow rate capacity than a typical range hood. So as wonderful as ERV/HRVs are, they won’t help with this issue.
The minimum code flow rate requirement for range hoods is 100 CFM. Makeup air is only required for exhaust range hoods having a flow rate of 400 CFM or larger and the code states:
“Exhaust hood systems capable of exhausting in excess of 400 CFM shall be provided with makeup air at a rate approximately equal to the exhaust-air rate. Such makeup-air systems shall be equipped with a means of closure and shall be automatically controlled to start and operate simultaneously with the exhaust system.”
So some would interpret the “...automatically controlled to start and operate...” language to preclude the use of manually opening windows, etc. to satisfy this requirement. However, there are several other ways to satisfy this issue:
First off, if you can get by using an exhaust range hood less than 400 CFM, you don’t need to provide any makeup air at all. If you can get by using a re-circulation range hood (even one having a flow rate much greater than 400 CFM) in lieu of an exhaust range hood, you also don't need to provide any makeup air at all since you are NOT exhausting any air.
If you need an exhaust range hood greater than 400 CFM, you can add an outside air duct that has an electrical/mechanical damper that is automatically controlled to open when the range hood is used. Some jurisdictions and inspectors like this air duct to be located in relative close proximity to the range hood it services. Some jurisdictions and inspectors are okay having this air duct be located anywhere in the building and this allows having this cold or hot outdoor air enter the building where it causes a less noticeable adverse comfort effect on building occupants and allows this outdoor air to get tempered as it flows through the building.
If you need an exhaust range hood greater than 400 CFM, you can also use a mechanical MAU (Makeup Air Unit) that is automatically activated whenever the range hood is activated. MAUs can also temper the cold or hot outside air using a heat exchanger like ERV/HRVs, but MAUs can be quite expensive like ERV/HRVs.