Two Diels-Alder type reactions, i.e., normal electron demand (NED) between 1,3-butadiene (BD) and acrolein (Acr) and inverse electron demand (IED) between 2,4-pentadienal (PDA) and methyl vinyl ether (MVE), have been investigated using the bonding evolution theory (BET). BET combines topological analysis of the electron localization function (ELF) and catastrophe theory. Catalyst effect has been incorporated through Lewis acid BH3. The B3LYP hybrid HF/DFT method along with 6-31G(d), 6-311++G(d,p) basis sets have been used. All reactions yield two-stage mechanism and there is no topological evidence that they might be concerted with two bonds partially formed during transition structure. A formation of six-membered ring requires 10 (or 11) steps separated by two types of catastrophes: fold and cusp. The first "intermolecular" bond (C1-C6) is formed at 1.93, 1.92 A (NED) and 1.92, 1.97 A (IED). The six-membered ring is "closed" at 2.11, 2.13 A (NED) and 2.5, 2.6 A (IED) via formation of the second bond C4-C5. All reactions begin with "reduction" of C=C bonds to single C-C (cusp catastrophes). Subsequently, the nonbonding electron density is concentrated (fold catastrophes) on terminal C atoms. Finally the new bonds, C1-C6 and C4-C5, are established (cusp catastrophes). Both magnitude and regularity of the electron redistribution, happening during reactions enable us to distinguish two effects: (1) the "ring effect", where a large amount of electron density is regularly transferred from double C=C bonds to intermolecular regions and single C-C bonds, (2) the "side chain effect"--usually weaker and irregular--involving substituents' bonds. In the transition structure, well formed bonding basin V(C1,C6), is observed only for the PDA...BH3/MVE reaction. For other reactions only the nonbonding basins: V(C1) and V(C6), are found in the interaction region C1...C6.