  Let $X$ be a smooth projective curve of genus $g\ge 3$ and $M_0$ be the
moduli space of rank 2 semistable bundles over $X$ with trivial determinant.
There are three desingularizations of this singular moduli space constructed by
Narasimhan-Ramanan \cite{NR}, Seshadri \cite{Se1} and Kirwan \cite{k5}
respectively. The relationship between them has not been understood so far. The
purpose of this paper is to show that there is a morphism from Kirwan's
desingularization to Seshadri's, which turns out to be the composition of two
blow-downs. In doing so, we will show that the singularities of $M_0$ are
terminal and the plurigenera are all trivial. As an application, we compute the
Betti numbers of the cohomology of Seshadri's desingularization in all degrees.
This generalizes the result of \cite{BaSe} which computes the Betti numbers in
low degrees. Another application is the computation of the stringy E-function
(see \cite{Bat} for definition) of $M_0$ for any genus $g\ge 3$ which
generalizes the result of \cite{kiem}.
