Do I need to caulk the joints of my stove pipe?

When I look at the joints of the pipe on my wood stove, I can
see that the there isn't a tight fit. Should I try to caulk this?
Won't the smoke come out there when the stove is going?

When a chimneyis drafting (i.e. when it is hot enough for the air
in it to raise) the smoke will not only go up, but air from the room
will be drawn into the spaces where the pipes join. If the smoke
comes out there, you either don't have the fire hot enough to
provide draft or the chimney is plugged.

The most common cause of a plugged chimney is a build up of
creosote on the chimney's spark arrestor. A quick look at the
chimney top should tell you if that is the problem.