  We use classical techniques to answer some questions raised by Daniele
Celoria about almost-concordance of knots in arbitrary closed $3$-manifolds. We
first prove that, given $Y^3 \neq S^3$, for any non-trivial element $g\in
\pi_1(Y)$ there are infinitely many distinct smooth almost-concordance classes
in the free homotopy class of the unknot. In particular we consider these
distinct smooth almost-concordance classes on the boundary of a Mazur manifold
and we show none of these distinct classes bounds a PL-disk in the Mazur
manifold, but all the representatives we construct are topologically slice. We
also prove that all knots in the free homotopy class of $S^1 \times pt$ in $S^1
\times S^2$ are smoothly concordant.
