In England you often hear "draw the curtains" for closing them and perhaps less frequently "draw back the curtain" for opening them. Twitching the curtains is what the elderly (like me) do to see who's outside without being seen oneself.
Maybe some people in the U.S. say 'draw the curtains', but it is not common. I learned this expression from a kids' book. Amelia Bedelia, the maid, doesn't understand what 'draw the curtains' means, so she draws a picture of them. :-)