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Let $E, F, E_0, E_1$ be rearrangement invariant spaces; let $a, \mathrm{b},\mathrm{b}_0, \mathrm{b}_1$ be slowly varying functions and $0<\theta_0,\theta_1<1$. We characterize the interpolation spaces$$\Big(\overline{X}^{\mathcal R}_{\theta_0,\mathrm{b}_0,E_0,\mathrm{a},F},\overline{X}^{\mathcalL}_{\theta_1,\mathrm{b}_1,E_1,\mathrm{a},F}\Big)_{\eta,\mathrm{b},E}\:, \quad0\leq\eta\leq1,$$ when the parameters $\theta_0$ and $\theta_1$ are equal(under appropriate conditions on $\mathrm{b}_i(t)$, $i=0,1$). This completesthe study started in \cite{Do2020,FMS-RL3}, which only considered the case$\theta_0<\theta_1$. As an application we recover and generalize interpolationidentities for grand and small Lebesgue spaces.

Reiteration Theorem for ${\mathcal R}$ and ${\mathcal L}$-spaces with the same parameter