Trying to Network at Summer Internship

I'm currently in 9 (of 15, i think?) of my internship, and I'm running into some real problems trying to make connections at work. I'm an IB/PE/HF hopeful, which is great since I'm currently an intern in alternative Asset Management which allows for some pretty great exposure. I've already been able to sit in on a few meetings w/BB, HF, and even some pretty cool "fringe" funds (dynamic beta, etc....basically things my office is a little too conservative for). Anyway, one of our main HF portfolios is managed by a top PE fund, and I get to sit in on the monthly update calls (there have been 2 so far that I've been in) and each time, I'm a silent participant (which is absolutely fine with me). The problem is, these calls are with my senior PM, who's a man of very few words, doesn't like digressing too much - even in calls where he's like BFFs with the MD, so he has ever even casually mentioned my name in passing or made the other end aware that I'm even there. Again, to clarify, this isn't like a personal affront to me or anything - just happy to be able to sit in and learn.

So, we had one of these update calls this morning, and again, no words from me or senior PM about my presence. Towards the end of the call, they mention they have an intern for the summer as well, and only mention it because she attends a rivalry school of both me and senior PM. I go back to my desk after the call, which was pretty early, so I didn't get to check my email as soon as I came in today, and I find that one of the analysts on the call reached out to me with some resources to get me caught up, at the request of one of the analysts in my division. A few presentations, some update letters, etc. Pretty cool stuff, definitely helpful for comprehension purposes.

On the email thread, both my senior PM and division analyst are copied. I have been working my ass off this whole summer following up with people I meet with, not to network behind my bosses' backs, but just to stay in touch so that I can hopefully network after the end of my internship. The problem is, I don't know if I should reply to this email, with like a quick thanks, would love to stay in touch, etc., because this is an active relationship (and a pretty big one) as opposed to all the others I've emailed in the past, which have just been like introductions or pitches from different managers.

I feel like this is a really good opportunity to have some kind of tangible coneection with this firm, but I don't want to overstep. Should I give a quick response? To just the analyst? or should I CC the firm's other analyst & MD? Should I CC my senior PM and the other analyst at my office as well? This may all seem pretty ridiculous, but our relationship with them is a working one...so I don't want to seem out of my place or anything.

tl;dr want to create a connection with an analyst at a massive, well-known PE firm (BC there are grounds to do so), but not sure if I can because it's a working relationship and I don't want to step on any toes. (help pls)