The previously proposed qualitative conceptualization of heavy-light- heavy (HLH) chemical reactions on a single potential energy surface (PES) as vibrationally nonadiabatic transitions at avoided crossings along the potential ridge lines is confirmed and further extended. An analytical as well as quantitative analysis of three-dimensional HLH reactions is carried out by applying the new semiclassical theory of nonadiabatic transition established by Zhu and Nakamura. About one thousand avoided crossings which appear in the sea of adiabatic potential curves obtained in the hyperspherical coordinate approach are classified into relevant and irrelevant ones for reactive transitions by introducing a certain diabatic decoupling procedure based on the dimensionless parameter of the new semiclassical theory. Thus about one hundred of three kinds of avoided crossings relevant for reactive transitions are specified and treated analytically. The cumulative reaction probabilities can be quite nicely reproduced quantitatively. This indicates that the clarification and conceptualization of reaction mechanisms can be done even analytically. State-to-state reaction processes can be qualitatively nicely comprehended as before, but cannot be quantitatively well reproduced, simply because inelastic transitions are not necessarily localized and cannot be well comprehended in terms of nonadiabatic transitions due to avoided crossings. An interesting series of avoided crossings responsible for rotationally inelastic transitions are found at energy lower than the threshold of reaction in the case of exo- or endoergic reaction.