  Anomalous X-ray Pulsars (AXPs) are now established to exhibit significant
X-ray variability and be prolific glitchers, with some glitches being
accompanied by large radiative changes. An open issue is whether AXP glitches
are generically accompanied by radiative changes, relevant for understanding
magnetar physical properties. Here we report on an analysis of archival X-ray
data from the AXP 1E~1841$-$045, obtained between 1993 and 2007. This AXP,
located in the center of SNR Kes~73, has exhibited three glitches between 2002
and 2007, as determined by {\it RXTE} monitoring since 1999. We have searched
for evidence of phase-averaged flux variability that could be present if
glitches in AXPs are usually accompanied by radiative changes. We find no
evidence for glitch-correlated flux changes from this source, arguing that such
behavior is not generic to AXPs.
