  Bringmann, Lovejoy, and Osburn showed that the generating functions of the
spt-overpartition functions spt(n), spt1(n), spt2(n), and M2spt(n) are
quasimock theta functions, and satisfy a number of simple Ramanujan-like
congruences. Andrews, Garvan, and Liang defined an spt-crank in terms of
weighted vector partitions which combinatorially explain simple congruences mod
5 and 7 for spt (n). Chen, Ji, and Zang were able to define this spt-crank in
terms of ordinary partitions. In this paper we define spt-cranks in terms of
vector partitions that combinatorially explain the known simple congruences for
all the spt-overpartition functions as well as new simple congruences. For all
the overpartition functions except M2spt(n) we are able to define the spt-crank
purely in terms of marked overpartitions. The proofs of the congruences depend
on Bailey's Lemma and the difference formulas for the Dyson rank of an
overpartition and the M2-rank of a partition without repeated odd parts.
