The top stay open enough to slide our 4 inch pipe through. The odd bit of moisture can come down the opening but gets evaporated right away.
I should add that a quick trip to the hardware store for a 3 or 4 foot section of insulated stove pipe is in order. Use this for the top section that passes close to combustables. Keep the tarp 6" away from it and good to go.
To build, lay 4 poles out evenly, tips to center. Ends away from center. Firmly lash tips together.
Use bailing wire to suspend the top section of your stove pipe with a good foot and a half sticking out top.
Once this is done, use a center pole and lift the T-P structure up from middle until it is the desired height.
Attach remainder of stove pipe down to stove.
Add more poles by simply leaning them. 3 more is good as 1 side will be your door flap. Anchor bases of all poles with rocks or dig small holes in ground for butt end
The center lifting pole can be removed, but keep it handy for tear down at the end of your trip.
Wrap the whole mess tightly with tarps and some overlap on the ground, leaving a door flap or entrance. Put debris or sod on overlap around tee pee bottom to prevent drafting.
My explanations probably make it sound super complicated but it's not.
This kind of structure will allow rain to roll off, snow to slide off, will stand up to winds ect. And it's a fun thing to build

Bring cord, ropes, a few good 16x20 tarps, bailing wire, ratchet straps, ground spikes ect
We also used to lash small straight poles across the main poles inside to hang wet socks, clothes ect.
Customizing a self made hunting structure is a lot of fun