Long exact sequence of homology of a triple

Definition
Suppose $$A \subset B \subset C$$ are topological spaces (each with the subspace topology from the bigger one). The long exact sequence of homology of this triple (usually denoted as $$(C;B,A)$$) is:

$$\ldots \to H_n(B,A) \to H_n(C,A) \to H_n(C,B) \to H_{n-1}(B,A) \to \ldots$$

where $$H_n(X,Y)$$ denotes the relative homology.

Particular cases
If $$A$$ is empty, we get the long exact sequence of homology of a pair, namely the pair $$(C,B)$$.

For homologies arising from a chain complex
If the homology theory involves homology of a chain complex $$Chain_.$$, then the above can be interpreted as the long exact sequence of homology arising from the following short exact sequence of relative chain complexes:

$$0 \to Chain_.(B,A) \to Chain_.(C,A) \to Chain_.(C,B) \to 0$$

In particular, this description works for singular homology, cellular homology and simplicial homology.