This is what I learned from here the post:
two interlocked circles are homeomorphic to two noninterlocked circles, thus they (two interlocked circles and two noninterlocked circles) are homotopic equivalent to each other.
but you cannot transform them; same for a knotted and an unknotted torus.
Q1: Can someone show that homeomorphism explicitly?
Q2: what is the name of the mathematical notion that distinguish the unlink(two noninterlocked circles) and the Hopf link(two interlocked circles)? Probably just the linking number? What else?
The comments have done a pretty good job of clearing up Q1: The homeomorphism between two linked and two unlinked circles is completely trivial: just map one circle to one circle, and the other circle to the other circle. What one really wants to distinguish the linked from the unlinked situation is that there is no homeomorphic mapping of $\Bbb R^3$ to $\Bbb R^3$ that takes the linked circles to the unlinked circles. Equivalently, one can consider whether there is a homeomorphism from $\Bbb R^3$ minus the linked circles to $\Bbb R^3$ minus the unlinked circles; there isn't, but if the linked circles could be unlinked then there would be.
The jargon term you are looking for in Q2 is ambient isotopy. This is yet another notion: It is a family $h_x$ of homeomorphisms from $\Bbb R^3$ to $\Bbb R^3$, where $x\in[0,1]$. $h_0$ must be the identity mapping, and $h_1$ must take the unlinked circles to the linked circles, and $h(x,p) = h_x(p)$ must be continuous on the product $[0,1]\times R^3$. The idea is that $h_0$ describes the starting position, and then $h_1$ describes the ending position, and the family of $h$es must go continuously from the starting position to the ending position. If the unlinked circles could be smoothly and continuously linked, there would be such a family of $h$es, but as they can't, there isn't.