Hello,

If you have a link of 2 components $U$ and $V$ in $S^3$. $U$ is the unknot, and you make $1/q$ dehn filling in $U$, you can visualize the resulting knot $V'$ from $V$, by twisting it $q$ times along a disc bounding $U$. How can I visualize $p/q$ dehn filling?. I mean, in that case after you do the filling you end up with a knot in the lens space $L(p,q)$, what knot $V'$ do you get in the universal covering $S^3$?

Thanks!