vents
Technically vent lines can tie together anywhere desired as long as the sizes correspond to the fixture loads. Legally, you cannot connect fixtures on one floor to the stack vent of the lower floors, although functionally there is no problem with doing so, again, assuming the pipe sizes are adequate. A fixture, such as a bathtub, with a high volume drainage discharge could create sufficient velocity during its descent that it could aspirate the water out of the toilet on the lower level, but a lavatory does not have that volume.