Ward Identity for Pair Pair Annihilation

The following Feynman Diagrams for the process $e^++e^-togamma+gamma$ are:

Knowing this I wrote the amplitude matrix:

$$M = -e^2epsilon^{*}_{mu}(p_3)epsilon^{*}_{nu}(p_4)bar{u}(p_2)left[frac{gamma^mu left(displaystyle{not} p_1 -displaystyle{not} p_3 – mright)gamma^nu}{(p_1 – p_3)^2 -m^2}+frac{gamma^nu left(displaystyle{not} p_1 -displaystyle{not} p_4 – mright)gamma^mu}{(p_1 – p_3)^2 -m^2} right]u(p_1).$$

I define $M$ as: $$ M = M^{mu nu}epsilon^{*}_{mu}(p_3)epsilon^{*}_{nu}(p_4),
$$ where $$M^{mu nu} = -e^2bar{u}(p_2)left[frac{gamma^mu left(displaystyle{not} p_1 -displaystyle{not} p_3 – mright)gamma^nu}{(p_1 – p_3)^2 -m^2}+frac{gamma^nu left(displaystyle{not} p_1 -displaystyle{not} p_4 – mright)gamma^mu}{(p_1 – p_3)^2 -m^2} right]u(p_1).$$

Now, I want to prove Ward’s Identity for this case so:

$$(p_3)_mu M^{mu nu} = 0 iff -e^2bar{u}(p_2)left[frac{displaystyle{not} p_3left(displaystyle{not} p_1 -displaystyle{not} p_3 – mright)gamma^nu}{(p_1 – p_3)^2 -m^2}+frac{gamma^nu left(displaystyle{not} p_1 -displaystyle{not} p_4 – mright)displaystyle{not} p_3}{(p_1 – p_3)^2 -m^2} right]u(p_1).$$

How do I go from here?

In the screenshot above, we see an example for Compton scattering. I tried to use the same idea but I don’t understand why from equation (3) to equation (4) the indices in the gamma matrices change.

Hope you can help me.