Mayer-Vietoris of pair (X,C)

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I would like to know if i can use Mayer-Vietoris with this form:

Let X be a topological space and A, B be two subspaces whose interiors cover X and $C\subset A\cap B$.

We get the exact sequence

$... \rightarrow H_q(A\cap B,C)\rightarrow H_q(A,C)\oplus H_q(B,C)\rightarrow H_q(X,C) \rightarrow ...$

It is true? i am trying to solve a problem of homology groups and i get stuck, and if this is true that could help me solve it, i would appreciate any comment

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1 Answer

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Yes, take $C = D = Y$ here:

For a proof, see p. 152 of Hatcher's Algebraic Topology.

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