You can add all the emails and all the links within them in the Clicked Link filter and use a Minimum Number of Times = 3 constraint.

However, with the above setup, there could be a case where a person would qualify for this filtering condition if they didn't click 3 unique links, i.e., they end up clicking the same link multiple times. To avoid this, you could do some complex setup where each email click is listened for, then you figure out who clicked in at least 3 of those assets (see combinations below, all of the 10 combinations should go in OR with each other).
- Clicked on A, B, and C Email links
- Clicked on A, B, and D Email links
- Clicked on A, B, and E Email links
- Clicked on A, C, and D Email links
- Clicked on A, C, and E Email links
- Clicked on A, D, and E Email links
- Clicked on B, C, and D Email links
- Clicked on B, C, and E Email links
- Clicked on B, D, and E Email links
- Clicked on C, D, and E Email links
Also, in general, sure managing transitions via a smart campaign instead is always a sane choice because of the flexibility and is a bit easier to manage, etc., if you're going with the method 1, i.e., use Min. Number of Time constraint, then you can use either to setup the transition - a smart campaign or a transition rule, but if you're planning to go with the latter, you'd need to go with the smart campaign as the transition rules only allow usage of ALL filtering logic for the filters.
Also, don't you have a scoring model/Revenue Stage modeler setup? I'd rather use those to manage the nurture transitions instead of such complicated setup as above.