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\author
Andrea Bruno \\ Kenji Matsuki
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\title
Log Sarkisov Program
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\abstract
The purpose of this paper is two-fold.  The first is to give a
tutorial
introduction to the so called Sarkisov program, a three-dimensional
generalization of Castelnuovo-Noether Theorem ``untwisting''
birational
maps between Mori tiber spaces, after Sarkisov, Reid, and Corti.
The second is an attempt to give a logarithmic generalization of the
program by introducing the notion of Sarkisov relation.

We also simplify and visualize the flowchart for the program, while
making explicit the necessary ingredients toward higher dimension.
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