  Let $A$ be a Nakayama algebra. We give a description of the singularity
category of $A$ inside its stable module category. We prove that there is a
duality between the singularity category of $A$ and the singularity category of
its opposite algebra. As a consequence, the resolution quiver of $A$ and the
resolution quiver of its opposite algebra have the same number of cycles and
the same number of cyclic vertices.
