  GW150914 marked the start of the gravitational wave (GW) era with the direct
detection of binary black hole (BBH) merger by the LIGO-Virgo GW detectors. The
event was temporally coincident with a weak signal detected by Fermi-GBM, which
hinted towards the possibility of electromagnetic emission associated with the
compact object coalescence. The detection of a short Gamma-Ray Burst (GRB)
associated with GW1708017, along with several multi-wavelength detections,
truly established that compact object mergers are indeed multi-messenger
events. The Cadmium Zinc Telluride Imager onboard AstroSat can search for X-ray
counterparts of the GW events and has detected over 600 GRBs since launch. Here
we present results from our searches for counterparts coincident with GW
triggers from the first three LIGO-Virgo-KAGRA (LVK) GW Transient Catalogs. For
72 out of 90 GW events for which AstroSat-CZTI data was available, we undertook
a systematic search for temporally coincident transients and we detected no
X-ray counterparts. We evaluate the upper limits on the maximum possible flux
from the source in a 100 s window centered around each trigger, consistent with
the GW localization of the event. Thanks to the high sensitivity of CZTI, these
upper limits are highly competitive with those from other spacecraft. We use
these upper limits to constrain the theoretical models that predict high-energy
counterparts to the BBH mergers. We also discuss the probability of
non-detections of BBH mergers at different luminosities and the implications of
such non-detections from the ongoing fourth observing run of the LVK detectors.
