Geodesic
Decomposition of a~birational map of three-dimensional varieties outside codimension~2
Izvestiya. Mathematics , Tome 21 (1983) no. 1, pp. 187-200

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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. 
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     title = {Decomposition of a~birational map of three-dimensional varieties outside codimension~2},
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Vik. S. Kulikov. Decomposition of a~birational map of three-dimensional varieties outside codimension~2. Izvestiya. Mathematics , Tome 21 (1983) no. 1, pp. 187-200. http://geodesic.mathdoc.fr/item/IM2_1983_21_1_a7/