There is no such thing as an air tight stove, for a fire in a stove we need Fuel and Air.
There are a number of different stoves manufactured to work with an external air intake for combustion.
It is very important to bring your Mechanical Heat Recovery / Ventilation Supplier on board by getting an assurance from them that the air pressure in the room where the stove is installed is not compromised.
One of the problems we have found in rooms without a permanent external air vent is the stoves can smoke when being lit or re-fuelled.
Some suppliers / installers of mechanical ventilation understand how their system should be set up to ensure the air pressure is at least equal, others dismiss the potential problem as a non issue.
Some consumers resort to opening windows when lighting or refuelling the stove to prevent smoke pouring into the room, it is not necessarily a bad stove or chimney / flue just a difference in air pressure between the sealed room and open flue.