Several qualitative notions of epistemic dependence between propositions are studied. They are closely related to the ordinal notion of conditional possibility. What this paper proposes is a systematic investigation of how the fact of learning a new piece of evidence individually affects previous beliefs. Namely a new piece of information A can either leave a previous belief untouched, or cancel it from the set of accepted beliefs, or even refute it. On the contrary, A can justify a new belief, not previously held, or fail to justify it. We provide axiomatizations of epistemic independence and relevance and show the close links between qualitative independence and the theory of belief change. It turns out that qualitative independence and AGM belief change operations have the same expressive power. Lastly, it is briefly suggested how qualitative independence can be applied to plausible reasoning.