Device of the type including an air inlet pipe fitted with at least one shutter flap connecting the building with the exterior. According to the invention, the device comprises: at least one flexible bag (4) made from an airtight material, placed in an enclosure (3) communicating with the interior (1) of the building to be supplied, the inner volume of the bag being connected with the exterior (E) of the building, through a passage (5) with a small cross-section; means for directly or indirectly connecting each bag (4) and each flap (6); and means (4, 8, 9, 10) for holding each shutter flap in a closed position while the pressure difference between the building interior and exterior does not exceed a predefined value, and for holding each shutter flap in an open position so long as the pressure difference between the building interior and exterior does not drop below another predefined value, less than the value required to open the flap.