Any command to connect to lines or any easy way to fill small gaps?

Hey, so i was just going about some cleanup with the linework for an animation, and was wondering if there was some way to connect small gaps in lines to make it easier to fill with the paintbucket too?  I know the union command makes them into the same object, but is there any way to set lines to connect if they're super close?

Note: Moderator combined Subject line above from duplicate post.