New relationship anxiety

So this is gonna sound stupid but I just started seeing this guy, well we've been seeing each other for a month and I know he likes me, we've talked about how much we enjoy being with each other. We're pretty open but there are days when he doesnt text me back after texting me constantly days before and I get anxiety like hes moved on or lost interest. Is it normal to have these kind of anxieties in a new relationship? I know he has a life past me just like i have work and interest past him. And Im not the kind of person to blow up your phone. If you dont text back Im not gonna text you again, Im very conscious about giving him his personal space. I guess Im waiting for the floor to drop and he decides he doesnt like me. Gosh I feel stupid. When/how do you get past the new relationship anxieties?