  We consider complete (possibly non-compact) three dimensional Riemannian
manifolds (M,g) such that: a) (M,g) is non-collapsed, b) the Ricci curvature of
(M,g) is bounded from below, c) the geometry of (M,g) at infinity is not too
extreme. Given such initial data (M,g) we show that a Ricci flow exists for a
short time interval. This enables us to construct a Ricci flow of any (possibly
singular) metric space (X,d) which arises as a Gromov-Hausdorff limit of a
sequence of 3-manifolds which satisfy a), b) and c) uniformly. As a corollary
we show that such an X must be a manifold.
