My Bryant furnace cycles several times before it will reach the set temp on the stat?

What is the condition of the filter?

Changed before XMAS

Watch the furnace when it cycles. If the burner actually goes out then you have a weak limit control or the furnace is overheating causing the burner to cut out.

OR post the exact model of your thermostat. If it is in recovery mode this can happen.

You should have a flashing light telling you if you have a fault. Check the small round window on the blower door of the furnace, you should see a flashing red light.