  Transition disks with small inner dust cavities are interesting targets for
the study of disk clearing mechanisms. Such disks have been identified through
a deficit in the infrared part of their SED, but spatially resolved millimeter
imaging is required to confirm the presence of an inner dust cavity. We use
high-resolution ALMA observations of 30 mas resolution in Band 6 continuum and
$^{12}$CO 2--1 emission of 10 transition disk candidates in the Lupus star
forming region, in order to confirm the presence of inner dust cavities and
infer the responsible mechanism. The continuum data are analyzed using
visibility modeling and the SEDs are compared with radiative transfer models.
Out of the six transition disk candidates selected from their SED, only one
disk revealed an inner dust cavity of 4 au in radius. Three of the other disks
are highly inclined, which limits the detectability of an inner dust cavity but
it is also demonstrated to be the possible cause for the infrared deficit in
their SED. The two remaining SED-selected disks are very compact, with dust
radii of only $\sim$3 au. From the four candidates selected from low-resolution
images, three new transition disks with large inner cavities $>$20 au are
identified, bringing the total number of transition disks with large cavities
in Lupus to 13. SED-selected transition disks with small cavities are biased
towards highly inclined and compact disks, which casts doubt on the use of
their occurrence rates in estimating dispersal timescales of photoevaporation.
Using newly derived disk dust masses and radii, we re-evaluate the
size-luminosity and $M_{\rm dust}-M_{\rm star}$ relations. These relations can
be understood if the bright disks are dominated by disks with substructure
whereas faint disks are dominated by drift-dominated disks. (Abridged)
