Beyond identifying genetic variants, we introduce a set of Boolean relations that allows for a comprehensive classification of the relations for every pair of variants by taking all minimal alignments into account. We present an efficient algorithm to compute these relations, including a novel way of efficiently computing all minimal alignments within the best theoretical complexity bounds. We show that for variants of the CFTR gene in dbSNP these relations are common and many non-trivial. Ultimately, we present an approach for the storing and indexing of variants in the context of a database that enables efficient querying for all these relations.