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In this paper, we introduce a non-rigid registration pipeline for unorganized point clouds that may be topologically different. Standard warp field estimation algorithms, even under robust, discontinuity-preserving regularization, produce erratic motion estimates on boundaries associated with ‘close-to-open’ topology changes. We overcome this limitation by exploiting backward motion: in the opposite direction, a ‘close-to-open’ event becomes ‘open-to-close’, which is by default handled correctly. Our approach relies on a general, topology-agnostic warp field estimation algorithm, similar to those employed in recent dynamic reconstruction systems from RGB-D input. We improve motion estimation on boundaries associated with topology changes in an efficient post-processing phase. Based on both forward and (inverted) backward warp hypotheses, we explicitly detect regions of the deformed geometry that undergo topological changes by means of local deformation criteria and broadly classify them as ‘contacts’ or ‘separations’. Subsequently, the two motion hypotheses are seamlessly blended on a local basis, according to the type and proximity of detected events. Our method achieves state-of-the-art motion estimation accuracy on the MPI Sintel dataset. Experiments on a custom dataset with topological event annotations demonstrate the effectiveness of our pipeline in estimating motion on event boundaries, as well as promising performance in explicit topological event detection.