  A study is made of charm and bottom flavor matching conditions on parton
densities. Starting from an $\bar{\rm MS}$ three-flavor density set, where the
scale $\mu < m_c$, and using the recently derived two-loop matching conditions,
we provide a new set of four-flavor parton densities where $ m_c \le \mu < m_b$
and five-flavor densities where $\mu \ge m_b$. The effect of the
next-to-next-to-leading order matching conditions on the evolution equations is
important for scales just above the transition regions. This includes the small
$x$ and small $Q^2$ domain studied by the H1 and ZEUS experiments at HERA. At
small $x$ the effects of the matching conditions never die away even for large
$\mu^2$.
