  The generic element of the moduli space of logarithmic connections with
parabolic points on holomorphic vector bundle over the Riemann sphere can be
represented by a Fuchsian equation with some singularities and some apparent
singularities. We analyze the case of rank $3$ vector bundle which leads to
third order Fuchsian equation. We find coordinates on an open subset of the
moduli space and we construct a non-trivial part of the moduli space by blowing
up along a variety in a special case.
