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It is well known that in q-matroids, axioms for independent spaces, bases,and spanning spaces differ from the classical case of matroids, since thestraightforward q-analogue of the classical axioms does not give a q-matroid.For this reason, a fourth axiom has been proposed. In this paper we show how wecan describe these spaces with only three axioms, providing two alternativeways to do that. As an application, we show direct cryptomorphisms betweenindependent spaces and circuits and between independent spaces and bases.

Alternatives for the $q$-matroid axioms of independent spaces, bases, and spanning spaces