Hey Tom,
I think everyone has their own idea about what constitutes a 'close friend', just like how they independantly feel about family members and 'closeness'.
For me, a close friend is someone I can count on in a pinch, but who doesn't smother me, and whom I don't smother. My best friend lives in Virginia (I'm in Vegas) and although we don't talk often, I know she would be there for me, as I would for her, in all occasions..good or bad. I can tell her anything, and she won't judge or ridicule me...things like that. As far as taking turns with the invites, when I lived there we did...but we also didn't 'count' i.e. sometimes I would ask her to go somewhere with me more often than she, mostly based on who was available at any given time.
I have numerous 'aquaintances' that I see more frequently, but it's much more of a hit-or-miss kinda thing. It is generally understood that reciprocation of invitations is expected, but again...it's hit or miss.
I hope this helps