We consider systems of f-functional monomers A(f), capable of thermoreversible associating with an equilibrium Arrhenius association constant k=g(0) exp(-E/T). Effects of the parameters f, g(0), and E on the global phase behavior of these systems are analyzed within two theoretical approaches differing in the way to allow for the presence of closed trails of labile bonds (cycles). Within the Flory approximation, which takes into account the trails closed at infinity only (i) sol-gel transition (emergence of the infinite cluster of labile bonds) is only a geometric transition; (ii) the phase diagrams with one, two, or three critical solution temperatures could exist; (iii) there are no diagrams with three phase coexistence temperatures (triple points). On the contrary, as consistent within our new mesoscopic cyclization (MsC) approach (i) the sol-gel transition is a genuine first order phase transition accompanied by a heat effect and phase separation; (ii) the phase diagrams are more varied and could possess triple points as well as some other peculiarities. An explicit topological classification of all types of phase diagrams is given for both approaches via building (i) the phase portraits, i.e., separation of the plane (ln g(0),E) into the regions corresponding to topologically similar phase diagrams, and (ii) typical phase diagrams on the (volume fraction, T) and (pressure, T) planes for all regions of these phase portraits. For MsC approach, the latent phase transition heats are also presented. Possible changes of the presented phase diagram classification for more complicated models (in particular, for systems with concurrent association) are discussed.