Our work is based on the Bluedisk project, a program to map the neutral gas in a sample of 25 HI-rich spirals and a similar number of control galaxies with the Westerbork Synthesis Radio Telescope (WSRT). In this paper we focus on the HI properties of the galaxies in the environment of our targeted galaxies. In total, we extract 65 galaxies from the WSRT cubes with stellar masses between $10^8M_{odot}$ and $10^{11}M_{odot}$. Most of these galaxies are located on the same HI mass-size relation and HI-plane as normal spiral galaxies. We find that companions around HI-rich galaxies tend to be HI-rich as well and to have larger R90,HI/R50,HI. This suggests a scenario of HI conformity, similar to the colour conformity found by Weinmann et al. (2006): galaxies tend to adopt the HI properties of their neighbours. We visually inspect the outliers from the HI mass-size relation and galaxies which are offset from the HI plane and find that they show morphological and kinematical signatures of recent interactions with their environment. We speculate that these outliers have been disturbed by tidal or ram-pressure stripping processes, or in a few cases, by accretion events.