The M=8.1, April 1st, 2014 Iquique earthquake, which broke part of the northern Chile seismic gap, was preceded by a strong foreshock sequence starting early January 2014. The reported analysis of the continuous records of the nearby GPS stations from the IPOC North Chili array lead to contradictory results concerning the existence and location of slow slip events (SSE) on the interplate contact. Resolving this controversy is an important issue, as although many SSEs are reported in subduction zones, only a few were found to be precursory to large earthquakes. Here we show that the records of a long base tiltmeter installed near Iquique, when corrected for coseismic steps, long term drift, tidal signals, and oceanic and atmospheric loading, show significant residual signals. These can be modelled with a sequence of four SSEs located close to Iquique. Their signature was already reported on some GPS stations, but their source was then characterized with a very low resolution in time and space, leading to contradicting models. With the tilt records, we can rule out the previously proposed models with a single large SSE closer to the mainshock. Combining tilt with GPS records greatly improves the resolution of GPS alone, and one could locate their sources 100 to 180 km south-southeast to the mainshock epicenter, with moment magnitudes between 5.8 and 6.2, at the edge of the main aftershock asperities. These moderate SSEs thus did not directly trigger the mainshock, but contributed to trigger the main foreshock and the main aftershock. Only the sensitivity and resolution of the tiltmeter, added to the GPS records, allowed us to describe with unprecedented accuracy this precursory process as a cascade of cross-triggered, short term aseismic slip events and earthquakes on the interplate contact. This three months of precursory activation appears to be the final acceleration burst of a weaker, longer term SSE which started mid-2013, already reported, with a moment release history which we could quantify. From the methodological point of view, our study takes advantage of an interesting complementarity of tilt and GPS measurements, due to their different dependence in distance to the source of strain, which turns out to be very efficient for resolving location and moment of strain sources, even when both instruments are close to each other. It finally demonstrates the efficient removal of sequences of small or even undetected coseismic steps from high resolution tilt record signal in order to retrieve the purely aseismic signal, a presently impossible task for high time resolution GPS records due to low signal to noise.