Which lines to clear/blow out for winter closing

You can except for the check valve before the pump. If you have to open that up anyway, you might as well blow from there so long as the hose fits.
It appears that with the valves sequenced correctly air could be blown through the circuit the correct way for the check valve.

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Is this the main drain for the pool?

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If so, while I believe technically you could sequence the valves to blow everything out from the SWG side, I question if you have enough air pressure to overcome the water in that line while blowing everything downstream of it. It may be easiest to just treat them as separate suction and return circuits and blow the returns from the SWG side and pull the check valve to blow the skimmer and drains from the suction side.
 
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