One of the most frustrating parts of moving into a new home or apartment is the furniture Tetris you have to play in order to squeeze all your big items around tight corners and stairways. Box springs can be particularly pesky, but they're so simply constructed that you can partially cut them in half. In this video from This Old House, Tom Silva shows how you can cut a box spring in half and fold it like a book. But it takes a little more finesse than literally just sawing the whole thing in half: After removing the bottom fabric, Tom makes two adjacent cuts on the long side of the outer wooden frame. Then they fold the box spring in half, carefully bending the metal wire that makes up most of the inner structure. When the box spring is moved into it's final destination, they unfold it back into shape, unbend the metal wires and carefully screw the wooden structure back together.
It's a fair amount of work, but you might not have any other option if you want to get that box spring wherever it needs to be. Better than cutting a mattress-shaped hole in the wall.
How to Move a Box Spring Up a Narrow Staircase [This Old House via YouTube]