If a guy I met online writes "You can ask me anything. I'm like an open book", is that a good or a bad thing?

That depends. If someone I was corresponding with on the Internet said that, I would run. Sounds like he's trying to convince you he's honest.

It's hard to tell. He has written that I can trust him a lot of times, but I don't trust him more cause he writes it.

I don't trust people easily, and it's not easy for me to trust people I meet online. But I feel kind of bad when I don't trust people. Perhaps they're the nicest person ever, or not.

I'd take someone saying 'i'm like an open book' as they have nothing to hide.

Which I think is a great thing. I know it's easier said than done, but if you build any kind of relationship from friendship to whatever you want with someone over the internet, then that's a good start. Just take it as read, and it's deffo a good thing.

It is just a phase, nothing more, nothing less, the issues will be if he is honest or not, you will not know that for months and checking on him latter.