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We present an extensive ($\sim$ 1200 d) photometric and spectroscopic monitoring of the Type IIn supernova (SN) 2012ab. After a rapid initial rise leading to a bright maximum (M$_{R}$ = $-$19.39 mag), the light curves show a plateau lasting about 2 months followed by a steep decline up to about 100 d. Only in the $U$ band the decline is constant in the same interval. At later phases, the light curves remain flatter than the $^{56}$Co decline suggesting the increasing contribution of the interaction between SN ejecta with circumstellar material (CSM). Although heavily contaminated by emission lines of the host galaxy, the early spectral sequence (until 32 d) shows persistent narrow emissions, indicative of slow unshocked CSM, and the emergence of broad Balmer lines of hydrogen with P-Cygni profiles over a blue continuum, arising from a fast expanding SN ejecta. From about 2 months to $\sim$1200 d, the P-Cygni profiles are overcome by intermediate width emissions (FWHM $\sim 6000$ \kms), produced in the shocked region due to interaction. On the red wing a red bump appears after 76 d, likely a signature of the onset of interaction of the receding ejecta with the CSM. The presence of fast material both approaching and then receding is suggestive that we are observing the SN along the axis of a jet-like ejection in a cavity devoid of or uninterrupted by CSM in the innermost regions., Comment: 8 Tables, 17 Figures. Accepted for publication in MNRAS