Love or fight? Awesome but scary show offered by two lizards in my yard!

Did you know that lizards fight like all other animals?
To tell the truth, I did not understand what lizards actually do in my yard, on a sunny spring day. I don't know if it's a fight for territory, or maybe for a partner, or maybe it's just a violent mating ritual. That's why if someone knows what's going on and why they're behaving like that, I'd like an explanation.
Sorry for the quality of the video but it was cold and I was shaking :(
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Enjoy!!!