Could someone explain, like just a geometric description, how the space $\displaystyle $\mathbb{R}^3\backslash A$$, where $\displaystyle $A$$ is the unit circle in the $\displaystyle $xy$$-plane, is homotopy equivalent to $\displaystyle $S^2\vee S^1$$, the one point union of a 2-sphere and a circle. I can't see it.