  We present the matching relations of the variable flavor number scheme at
next-to-leading order, which are of importance to define heavy quark partonic
distributions for the use at high energy colliders such as Tevatron and the
LHC. The consideration of the two-mass effects due to both charm and bottom
quarks, having rather similar masses, are important. These effects have not
been considered in previous investigations. Numerical results are presented for
a wide range of scales. We also present the corresponding contributions to the
structure function $F_2(x,Q^2)$.
