A prediction of the classic active galactic nuclei (AGN) unification model is the presence of ionisation cones with different orientations depending on the AGN type. Confirmations of this model exist for present times, but it is less clear in the early Universe. Here, we use the morphology of giant Ly$alpha$ nebulae around AGNs at redshift z$sim$3 to probe AGN emission and therefore the validity of the AGN unification model at this redshift. We compare the spatial morphology of 19 nebulae previously found around type I AGNs with a new sample of 4 Ly$alpha$ nebulae detected around type II AGNs. Using two independent techniques, we find that nebulae around type II AGNs are more asymmetric than around type I, at least at radial distances $r>30$~physical kpc (pkpc) from the ionizing source. We conclude that the type I and type II AGNs in our sample show evidence of different surrounding ionising geometries. This suggests that the classical AGN unification model is also valid for high-redshift sources. Finally, we discuss how the lack of asymmetry in the inner parts (r$lesssim$30 pkpc) and the associated high values of the HeII to Ly$alpha$ ratios in these regions could indicate additional sources of (hard) ionizing radiation originating within or in proximity of the AGN host galaxies. This work demonstrates that the morphologies of giant Ly$alpha$ nebulae can be used to understand and study the geometry of high redshift AGNs on circum-nuclear scales and it lays the foundation for future studies using much larger statistical samples.
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