The landings are all trapped with a time-delayed Spark. On a fast enough system you'll usually be able to run across the landings without being hit. You can also X-jump, Spell Jump or Levitate past them.
These rooms are easier to clean out from the bottom. If you only cleared one stairwell before going up then Monsters from the second will be waiting for you when you come back down. You can get ahead of them if you remember that you don't need to use the stairs on the way down -- that's what Featherfall is for.