We consider the Angenet-Caputo-Knopf's Ricci flow through non-degenerate neckpinch singularities. We will explain how one can see the A-C-K's Ricci flow through a neckpinch singularity as a flow of integral current spaces. We then prove the continuity of this weak flow with respect to the Sormani- Wenger Intrinsic Flat (SWIF) distance.