Ontology alignment is an area of active research where many algorithms and approaches are being developed. Their performance is usually evaluated by comparing the produced alignments to a reference alignment in terms of precision, recall and F-measure. These measures, however, only provide an overall assessment of the quality of the alignments, but do not reveal differences and commonalities between alignments at a finer-grained level such as, e.g., regions or individual mappings. Furthermore, reference alignments are often unavailable, which makes the comparative exploration of alignments at different levels of granularity even more important. Making such comparisons efficient calls for a 'human-in-the-loop' approach, best supported through interactive visual representations of alignments. Our approach extends a recent tool, Matrix Cubes, used for visualizing dense dynamic networks. We first identify use cases for ontology alignment evaluation that can benefit from interactive visualization, and then detail how our Alignment Cubes support interactive exploration of multiple ontology alignments. We demonstrate the usefulness of Alignment Cubes by describing visual exploration scenarios, showing how Alignment Cubes support common tasks identified in the use cases.