A Toroidal Paradox

In a beautiful puzzle, Martin Gardner considered the two linked surfaces shown below in the figure 1. The surfaces can be stretched or shrunk in any desidered way, provided there is no tearing or sticking together of separate parts.

Can the two-hole torus be deformed so that one hole becomes unlinked as is shown in figure 2?


(see: Gardner, Martin. The last recreations: hydras, eggs, and other mathematical mystifications. Springer Science & Business Media, 2007; 336-337)

SPOILER ALERT: The animation below shows how to perform the trick.

by gmt, oct2020