Definition of excisive triad: $(X;X_1,X_2)$ is an excisive triad if the inclusion $(X_1,X_1\cap X_2)\rightarrow (X,X_2)$ induces isomorphism in relative homology.
The definition is not symmetric in $X_1$ and $X_2$, but I would like to show if $(X;X_1,X_2)$ is an excisive triad then so is $(X;X_2,X_1)$ from the axiom. I try the following triple sequences in $X,X_1,X_1\cap X_2$ and $X,X_2,X_1\cap X_2$:
The green arrows are isomorphisms by assumption and we would like to show the red arrows are isomorphisms. We can split the two triple sequences, so I know the red is composite of mono and epi. But now I get stuck. What further information can we deduce from this?