TL;DR
There are two fancied-up iii-vi-ii-V progressions in F and Gb major, respectively.
The chord symbols in this case are an attempt to give a more-or-less literal translation of the written chord — that is, indicating all of the pitches present — rather than a functional one.
To begin deciphering them, note that in the first measure F is a pedal tone, and in the second measure, Ab is a pedal tone.
Considering that F is not a chord tone in each case, leaves us with
A-7b5 – Ab-7b5 — G-7(add11) — C-7
However, the C in the G-7(add11) is also not a functional pitch. It's an anticipation of the resolution to the following C-7. Thus:
A-7b5 — Ab-7b5 — G-7 — C-7
Or, even more simply
A-7 – Ab-7 – G-7 – C-7
A similar process allows for simplification of the second measure. The first chord reduces to Bb-7
, the second to Ao7
, the third to Ab-7
, and the fourth to Db7
, which resolves into GbM7
.
Bb-7 – Ao7 — Ab-7 — Db7 — GbM7
Now, allowing that the second chord in each measure is a tritone substitution, we have something like
F: iii — vi — ii — V
Gb: iii — vi — ii — V — I