Identifying three kinds of "unity" in Kant's "Critique of Pure Reason"

It's kind of hard guess which passages you're referring to. Are you talking of §16 of the transcendental deduction (B-Edition)?

In it Kant speaks of the Original Synthetic Unity of Apperception. Here the unity of consciousness is explored as a synthetic unity, which is constituted by the accompaniment of all our thoughts by "I think". Only by recognizing each representation as my own they do appear linked, The "I think" in itself appears as an act of spontaneity, transcendental "act of the mind" as introduced on page A102.

The "I" in this concept or judgement "I think" is the transcendental subject. We find it in any given thought 'as' thought without adding to the thought content, but in the realization that this is something we experience. Since that means the thought and the representations in it have to be constituted form a multitude of sensations and affectations by bringing them into the order of spacetime, we have to acknowledge that unity is synthetic. That means any object we're conscious off is in itself a synthetic unity (is that your #3)?

While consciousness itself (that is, any given empirical consciousness =? #2) is in itself a synthetic unity, falling under the same quasi-concept of "I-think", each representation we'e conscious of must be understood as in itself containing a multitude of sub-notions that are themselves again in our consciousness, with more or less awareness. This is the unity of the object (=? #1).

Since any concept is - as an act of thought - itself an act of combination (=synthesis) but also an analytical unity to the notions and representations that contain it as a property, the same holds for "I think" - although Kant states that this notion has "no special designation" (A341)

I think one could distinguish :

• unity as a special category ( unity, plurality, totality)

• unity as " originally synthetic unity of aperception"; this unity is " transcendental" in the original sense, that is, above all categories

• unity as Idea of Reason ( imaginary focus at which Reason is aiming in its effort directed at the " unconditionned " or "absolute")