The main goal of this paper is
to develop a constructive factorization method for a bimeromorphic morphism
between smooth germs of complex analytic spaces of dimension 3 provided is
composition of blowing-ups with smooth, closed and irreductible centers. The
factorization is determined by the irreductible components of the morphism’s
exceptional divisor. This result may be used for instance to prove the invariance of
the characteristic pairs of quasi-ordinary singularities.