hold or host

催す(もよおす)	To host a small event – a party, for instance. Unlike 主催、　催す has the idea that you’re responsible for what happens, rather than just giving money to the event.

主催(しゅさい)	To sponsor a large event. “This golf tournament is brought to you by Penzoil.”

開催(かいさい)	To open a huge event. The opening ceremonies. “Is that expo open yet?”