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We present an analysis of morphological, kinematic and spectral asymmetries in observations of atomic neutral hydrogen (HI) gas from the Local Volume HI Survey (LVHIS), the VLA Imaging of Virgo in Atomic Gas (VIVA) survey and the Hydrogen Accretion in Local Galaxies Survey (HALOGAS). With the aim of investigating the impact of the local environment density and stellar mass on the measured HI asymmetries in future large HI surveys, we provide recommendations for the most meaningful measures of asymmetry for use in future analysis. After controlling for stellar mass, we find signs of statistically significant trends of increasing asymmetries with local density. The most significant trend we measure is for the normalised flipped spectrum residual ($A_{\mathrm{spec}}$), with mean LVHIS and VIVA values of $0.204\pm0.011$ and $0.615\pm0.068$ at average weighted $10^{\mathrm{th}}$ nearest-neighbour galaxy number densities of $\log(ρ_{10}/\mathrm{Mpc}^{-3})=-1.64$ and 0.88, respectively. Looking ahead to the WALLABY survey on the Australian Square Kilometre Array Pathfinder (ASKAP), we estimate that the number of detections will be sufficient to provide coverage over 5 orders of magnitude in both local density and stellar mass increasing the dynamic range and accuracy with which we can probe the effect of these properties on the asymmetry in the distribution of atomic gas in galaxies.