Convergence of Ricci flow solutions to Taub-NUT

We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric g(0) on R-4 with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If g(0) has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric g(TNUT) in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when g(0) is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for g(TNUT):