quantum field theory - Gauge-invariance of pole mass using Ward Identity

I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter.

But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of the poles in Greens functions are gauge-independent to all orders?

The difficulty I'm running into is in using the identities to make statements about the analytic structure of Green's functions.