I'm new to the website and I'd like to thank anyone that write here because it's very helpful.

Can someone help me figure out ranges and math in this hand? I'm new to the math aspect and I need to know if I'm thinking in the right way...

Villain is a decent reg and he had AKo.

UTG (Villain) range:
I started considering a standard UTG opening range (55+, AJo+, KQo, T9s, JTs, QTs+, KTs+, ATs+) and then, since he checked back the flop, I removed the hands that are Cbetting (55+, T9s). The hands still in his range that are raising my bet on the turn are KQo, AKo, KTs+, AKs.

SB (Hero) range:
My SB calling range vs UTG is (22-JJ, KQo, AJ-AQo, T9s, JTs, QTs+, KTs+, AT-AJs) (I removed 3-betting hands). On the flop I'm checking 100% of my range. On the turn I'm betting something like 75% of all my hands but I'm not sure about the exact range. After his raise, I'm going all-in with (55, 66, 99, KT-KQclubs).

If ranges are correct, the equity after the shove is 87% in my favour and, considering the size of the pot, the all-in needs to work about 80% of the time. So i would need to add some bluffs as well (?). I'm not sure if the shove is better than a simple re-raise.
On the analisys I'm missing the fact that sometimes he's checking back a moster (top set) on the flop and sometimes Cbetting with AK.

Thanks!