Decomposition of a birational map of three-dimensional varieties outside codimension 2

The main result is the proof of the fact that one can perform a finite number of monoidal transformations with nonsingular centers in such a way that any two nonsingular birationally isomorphic threefolds become isomorphic outside codimension $2$, and the subsets at which the varieties are not isomorphic consist of unions of nonsingular rational curves transversally intersecting with each other.
Bibliography: 8 titles.