開く vs 開ける(ひらく vs あける vs あく)

The Difference:
開く (ひらく) = open (like a flower, open in a spreading motion), transitive and intransitive
開ける = open (like a bottle), transitive
開く (あく) = open (like a bottle), intransitive
Ex:
手をひらく = open your hand (like a flower)
When it comes to businesses:
開く (ひらく) = open (a new business, business didn’t exist before)
開ける = open (for business for the day, from closed to open)
Ex:
店をひらく Open a shop in the sense of establish it and begin trading.
店をあける Open the shop for the day. Open the doors.

source: https://learnjapaneseonline.info/2018/09/18/finding-the-right-opening-%E9%96%8B%E3%81%8F-%E3%81%82%E3%81%8F-vs-%E9%96%8B%E3%81%8F-%E3%81%B2%E3%82%89%E3%81%8F-vs-%E9%96%8B%E3%81%91%E3%82%8B-%E3%81%82%E3%81%91%E3%82%8B/