  We find the automorphism group of the moduli space of parabolic bundles on a
smooth curve (with fixed determinant and system of weights). This group is
generated by: automorphisms of the marked curve, tensoring with a line bundle,
taking the dual, and Hecke transforms (using the filtrations given by the
parabolic structure). A Torelli theorem for parabolic bundles with arbitrary
rank and generic weights is also obtained. These results are extended to the
classification of birational equivalences which are defined over "big" open
subsets (3-birational maps, i.e. birational maps giving an isomorphism between
open subsets with complement of codimension at least 3).
  Finally, an analysis of the stability chambers for the parabolic weights is
performed in order to determine precisely when two moduli spaces of parabolic
vector bundles with different parameters (curve, rank, determinant and weights)
can be isomorphic.
