I'm a bit new to knot theory and I'm trying to exchange the two components of a Whitehead link (below) by using only a series of isotopies. I'm able to see how the knot gets unknoted and becomes the circle but still fail to see how the circle part can transform into the knot by an isotopy, any help would be appreciated.
Consider the following series of isotopies:
Rotate the inner most loop
And again
Pull out the inner "loop"
Begin rotating the left twist around the circle
Rotate further
Move the top arc to the inside
Stretch everything to make it look "nice"