  We consider the space of ordered pairs of distinct $\mathbb{C}P^1$-structures
on Riemann surfaces (of any orientations) which have identical holonomy, so
that the quasi-Fuchsian space is identified with a connected component of this
space. This space holomorphically maps to the product of the Teichm\"uller
spaces minus its diagonal.
  In this paper, we prove that this mapping is a complete local branched
covering map. As a corollary, we reprove Bers' simultaneous uniformization
theorem without any quasi-conformal deformation theory. Our main theorem is
that the intersection of arbitrary two Poincar\'e holonomy varieties (${\rm
SL}_2\mathbb{C}$-opers) is a non-empty discrete set, which is closely related
to the mapping.
