  This is the first of a series of papers on the long-time behavior of 3
dimensional Ricci flows with surgery. In this paper we first fix a notion of
Ricci flows with surgery, which will be used in this and the following three
papers. Then we review Perelman's long-time estimates and generalize them to
the case in which the underlying manifold is allowed to have a boundary.
Eventually, making use of Perelman's techniques, we prove new long-time
estimates, which hold whenever the metric is sufficiently collapsed.
