The classical notion of a quasi-proper map is as follows. Let \(\pi \colon M \rightarrow N\) be a holomorphic map between reduced complex spaces. The map \(\pi \) is quasi-proper at a point \(y_0 \in N\) when there exists an open neighborhood W of \(y_0\) in N and a compact set K in M such that for all \(y \in W\) and every irreducible component C of \(\pi ^{-1}(y)\) we have \(K \cap C \neq \emptyset \) .