Can I leave the air vents open?

Air vents being open is absolutely fine and is also better for your liner as it avoids burning fuel at low temperatures and thus creates less soot.  Stoves suitable for smoke exempt areas have air vents that are permanently open for precisely this reason.

Vents that are fully open all the time will mean the fire is roaring constantly however, so a good idea to get a  stove thermometer to ensure that you are not burning your stove too hot. You don’t have to spend a lot for one of these and they really do help.