A general multipoint boundary value problem for non-uniformly $2b$-parabolic equations with degeneration is studied. The coefficients of the parabolic equations and boundary conditions admit power degeneracy of arbitrary order in the time variable and the spatial variables on a certain set of points. To solve the posed multipoint boundary value problem, solutions of problems with smooth coefficients in Hölder spaces with the corresponding norm are studied. Using interpolation inequalities and a priori estimates, estimates of the solution of auxiliary problems and their derivatives in special Hölder spaces are established. Using the Riesz and Archel theorems, a convergent sequence is distinguished from the compact sequence of solutions of auxiliary problems, the limiting value of which is the solution of a multipoint time boundary value problem for a $2b$-parabolic equation with degeneration. The estimates of the solution of the posed problem are established in Hölder spaces with power-weight. The order of the power-weight is determined by the order of singularities of the coefficients of the equations and boundary conditions. With certain restrictions on the right-hand side of the equation and boundary conditions, an integral representation of the posed problem is obtained.

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