Monomialization of Morphisms from 3-Folds to Surfaces

A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e''tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S.
The construction is very explicit and uses technique...