Relaxation of tensile strain in AlGaN heterostructures grown on GaN template can lead to the formation of cracks. These extended defects locally degrade the crystal quality resulting in a local increase of non-radiative recombinations. The effect of such cracks on the optical and structural properties of core-shell AlGaN/AlGaN multiple quantum wells grown on GaN microwires are comprehensively characterized by means of spectrally and time-correlated cathodoluminescence (CL). We observe that the CL blueshifts near a crack. By performing 6x6 k.p simulations in combination with transmission electron microscopy analysis, we ascribe this shift to the strain relaxation by the free surface near cracks. By simultaneously recording the variations of both the CL lifetime and the CL intensity across the crack, we directly assess the carrier dynamics around the defect at T = 5 K. We observe that the CL lifetime is reduced typically from 500 ps to less than 300 ps and the CL intensity increases by about 40% near the crack. The effect of the crack on the optical properties is therefore of two natures. First, the presence of this defect locally increases non-radiative recombinations while at the same time, it locally improves the extraction efficiency. These findings emphasize the need for time-resolved experiments to avoid experimental artifacts related to local changes of light collection