Rule 1 – the Downright Rule: to swap any two throws in a pattern, the throw that moves to the right decreases with each step, and the throw that moves to the left increases with each step. A throw may not move if it would decrease below zero.

Take for example the pattern 51234. Let’s swap the red and blue throws: 51234. The red throw moves two steps to the right, so it decreases by two, while the blue throw moves two to the left, so it increases by two: 51234  41334.

This is how it works: the transformation moves the throws but leaves the catches in the same place. The blue throw is made two beats earlier, so it is in the air for two beats more; the red throw is made two beats later, so it is in the air for two beats less.

Let’s attempt to swap two different throws: 51234. The red throw moves three to the right, so you subtract three. This would give –2, so it is not allowed. But you can swap these throws if you use the following rule first.

Rule 2 – the Circular Rule: a throw may be moved from the front to the back of a pattern.

Using rule 2 you can transform 5123412345234513451245123. All these patterns are identical. So 51234 can be changed to 45123. Now the blue throw can move to the right, and decrease by two, while the red throw moves to the left, and increases by two: 
45123  35223.