We prove some equivalence formulas for the K functional for three spaces. In particular we calculate K(t, s, f, L_p0, L_p1, L_p2). We also give an integral formula connecting the K functional for triples of the type (A₀, A₁, A₂), where A₁ is of class C(θ, A₀,A₂), with the K functional for the pair (A₀, A₂). This formula is used to prove a reiteration formula for interpolation of the triple (A₀, A_l, A₂) when Ai is of class C(θ_i, X, Y)