  We provide a definition of ephemeral multi-persistent modules and prove that
the quotient of persistent modules by the ephemeral ones is equivalent to the
category of $\gamma$-sheaves. In the case of one-dimensional persistence, our
definition agrees with the usual one showing that the observable category and
the category of $\gamma$-sheaves are equivalent. We also establish isometry
theorems between the category of persistent modules and $\gamma$-sheaves both
endowed with their interleaving distance. Finally, we compare the interleaving
and convolution distances.
