We built a pergola, is it safe?
Well, it seems totally safe to me, it's not going to fall on you unprovoked. You won't be able to drive a truck into it, but you can sit under it. You can't land an aircraft on it, but it should be able to handle the rain and snow. It's not really load bearing, and it looks beautiful.

However, if you're afraid, grab a Kreg joint kit and screw them together at the notches. Do it from the sides, 1/3rd of the way from the edge to the notch. You can put a dowel in the hole, cut it off, sand it down and you'll barely be able to tell anything's there.