Given E_0, E_1, F_0, F_1, E rearrangement invariant function spaces, a_0, a_1, mathrm {b}_0, mathrm {b}_1, mathrm {b} slowly varying functions and 0< theta _0<theta _1<1, we characterize the interpolation spaces (X¯θ0,b0,E0,a0,F0R,X¯θ1,b1,E1,a1,F1R)θ,b,E,(X¯θ0,b0,E0,a0,F0L,X¯θ1,b1,E1,a1,F1L)θ,b,E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\big ({\\overline{X}}^{{\\mathcal {R}}}_{\ heta _0,\\mathrm {b}_0,E_0,a_0,F_0}, {\\overline{X}}^{{\\mathcal {R}}}_{\ heta _1, \\mathrm {b}_1,E_1,a_1,F_1}\\big )_{\ heta ,\\mathrm {b},E},\\quad \\big ({\\overline{X}}^{{\\mathcal {L}}}_{\ heta _0, \\mathrm {b}_0,E_0,a_0,F_0}, {\\overline{X}}^{\\mathcal L}_{\ heta _1,\\mathrm {b}_1,E_1,a_1,F_1}\\big )_{\ heta ,\\mathrm {b},E} \\end{aligned}$$\\end{document}and (X¯θ0,b0,E0,a0,F0R,X¯θ1,b1,E1,a1,F1L)θ,b,E,(X¯θ0,b0,E0,a0,F0L,X¯θ1,b1,E1,a1,F1R)θ,b,E,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\big ({\\overline{X}}^{{\\mathcal {R}}}_{\ heta _0,\\mathrm {b}_0,E_0,a_0,F_0}, {\\overline{X}}^{{\\mathcal {L}}}_{\ heta _1, \\mathrm {b}_1,E_1,a_1,F_1}\\big )_{\ heta ,\\mathrm {b},E},\\quad \\big ({\\overline{X}}^{{\\mathcal {L}}}_{\ heta _0, \\mathrm {b}_0,E_0,a_0,F_0}, {\\overline{X}}^{\\mathcal R}_{\ heta _1,\\mathrm {b}_1,E_1,a_1,F_1}\\big )_{\ heta ,\\mathrm {b},E}, \\end{aligned}$$\\end{document}for all possible values of theta in [0,1]. Applications to interpolation identities for grand and small Lebesgue spaces, Gamma spaces and A and B-type spaces are given.