  Partition identities are often statements asserting that the set $\mathcal
P_X$ of partitions of $n$ subject to condition $X$ is equinumerous to the set
$\mathcal P_Y$ of partitions of $n$ subject to condition $Y$. A Beck-type
identity is a companion identity to $|\mathcal P_X|=|\mathcal P_Y|$ asserting
that the difference $b(n)$ between the number of parts in all partitions in
$\mathcal P_X$ and the number of parts in all partitions in $\mathcal P_Y$
equals a $c|\mathcal P_{X'}|$ and also $c|\mathcal P_{Y'}|$, where $c$ is some
constant related to the original identity, and $X'$, respectively $Y'$, is a
condition on partitions that is a very slight relaxation of condition $X$,
respectively $Y$. A second Beck-type identity involves the difference $b'(n)$
between the total number of different parts in all partitions in $\mathcal P_X$
and the total number of different parts in all partitions in $\mathcal P_Y$. We
extend these results to Beck-type identities accompanying all identities given
by Euler pairs of order $r$ (for any $r\geq 2$). As a consequence, we obtain
many families of new Beck-type identities. We give analytic and bijective
proofs of our results.
