The transmission spectra of many hot Jupiters show signatures of high-altitude aerosols. One suggested mechanism for forming these aerosols is that photochemical processes generate hazes on the dayside. We present simulations of the hot Jupiter HD 189733b using a three-dimensional general circulation model (MITgcm). We use passive tracers to represent photochemical hazes in order to study how hazes are transported by atmospheric circulation. Haze particles in our model are spherical with a constant size. The results show that the haze mass mixing ratio varies horizontally by over an order of magnitude. The behavior is characterized by two regimes: small particles (<30 nm; dynamical mixing dominates) and large particles (>30 nm; gravitational settling dominates). In the small-particle regime, hazes accumulate in two large mid-latitude vortices on the night side. Because these vortices extend across the morning terminator, more hazes are present at the morning terminator than at the evening terminator. In the large-particle regime, hazes settle out quickly on the nightside, resulting in more hazes at the evening terminator. We examined if differences between evening and morning terminator could be observed with transmission spectroscopy through ingress and egress spectroscopy, focusing on the small-particle regime. Terminator differences in haze mass mixing ratio and temperature considered each by themselves can result in significant differences in the transit spectra of the terminators. When combining both effects for HD189733b, however, they largely cancel out each other, resulting in very small terminator differences in the spectra. Terminator differences in transit, if observable at all, will therefore be difficult to interpret because there is a degeneracy between temperature and the haze distribution in fits to the transit data. Furthermore, transit spectra based on the GCM-derived haze distribution fail to reproduce the steep spectral slope at short wavelengths in the current transit observations of HD 189733b. The spectral slope can, however, be reproduced if mixing through small-scale turbulence not resolved by the GCM is enhanced. In this scenario, an inhomogeneous haze distribution across the terminator arises as well.