Let us remind that in order to study a scattering amplitude $A(s,t)$ in the Regge kinematics $s \gg -t$ (where $s$ and $t$ are the standard Mandelstam variables), it is convenient to represent $A(s,t)$ in the following form: $A(s,t) = A^{(+)}(s,t)+ A^{(-)}(s,t)$, with $ A^{(\pm)}(s,t) = (1/2)[A(s,t) \pm A(-s,t)]$ called the positive (negative) signature amplitudes. We shall consider only amplitudes with the positive signatures. The IREE for the negative signature electroweak amplitudes can be obtained in a similar way, see e.g. Ref. [@egt] for more details.

The paper is organized as follows: in Sect. 2 we define the kinematics and express the scattering amplitude for the $e^+e^-$ annihilation in terms of invariant amplitudes. In Sect. 3, we construct the evolution equations for the invariant amplitudes for the case when in the center mass (cm) frame, the scattering angles are very small. First, we obtain the IREE equations in the integral form and then we transform them in the simpler, differential form. These differential equations are solved in Sect. 4 and explicit expressions for the invariant amplitudes involving the Mellin integrals are obtained. In Sect. 5, we consider the case of large scattering angles, or when the Mandelstam variables s, t 