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I already think that Arsenal are champions for this year and for real now , they are the better team in EPL right now. City ...they are focused on winning UCL , I have no doubts about it so their games in EPL won't have the same intensity like their UCL games.
The advantage is there for Arsenal, of course. I think you are also right about Arsenal's chances because the Premier League is the only focus they will be fighting for. Meanwhile Manchester City will still share their focus on three different competitions including the Premier League, Champions League and FA Cup.
Because of that, Manchester City might lose their chance in the Premier League considering that Arsenal will really want to maintain their consistency at the top of the table. There is a chance for Manchester City, but I think it's too small to be expected to knock Arsenal off the top.
Regarding City vs Liverpool, I could see this game ending with a draw as neither of them want to lose points but a bigger chance for City to actually win the game because Liverpool are still a shaky team this year with massive ups and downs.
A draw is a possibility, but in any case I'm sure Manchester City will do their best not to be too far from Arsenal. Whatever City's unsatisfactory results in this match will only bring them closer to the fact that the Premier League is not for them this season.