Prove for any homology theory ($H_*, \partial_*$) with values in R-mod that satisfies the dimension axiom there is an isomorphism $H_n(X,A)$ $\cong$ $\tilde H_n(X/A)$ where $A$ $\subset$ $X$ is a closed subspace which is a neighborhood deformation retract.
My approach was to use the Meyer-Vietoris- sequence for pushouts which gives us $H_n(X,A)$ $\cong$ $H_n(X/A, pt)$ for all n.
Furthermore I applied the long exact sequence for pairs to $(X/A, pt)$ and we get $H_n(X/A)$ $\cong$ $H_n(X/A, pt)$ for all n except n=1 and n=0. Also we have $\tilde H_n(X/A)$ $\cong$ $H_n(X/A)$ for all n except n = 0.
Now I am stuck for n=0 and n=1. Any hints?