The following result is due to Grothendieck and Artin and can be found in SGA 1. Let $X$ be a normal scheme of finite type over $\mathbb{C}$. Let $\mathfrak{X}'$ be a normal complex analytic space, together with a finite morphism $\mathfrak{f}: \mathfrak{X}' \to X_h$. (We define a **finite** morphism of analytic spaces to be a proper morphism with finite fibers.) Then there is a unique normal scheme $X'$ and a finite morphism $g: X' \to X$ such that $X_h' \cong \mathfrak{X}'$ and $g_h = \mathfrak{f}$.

I was wondering if anybody could supply me their intuition behind Grothendieck and Artin's proof of the Riemann existence theorem in this generality?