We define $F_{m,n}{(M)}=\{(z_1,z_2,\dots,z_n) \in \prod_{i=1}^{n}{(M-Q_m)}|z_i \neq z_j, i \neq j\}$, where M is a manifold(connected) and $Q_m$ be a set of fixed distinguished points of $M$.
How can be picking $n$ distinct points from a Manifold with $m$ punctures be same as picking $m$ distint points from a manifold with $n$ punctures?