We trace the full evolution of low- and intermediate-mass stars (1 ≤ M ≤ 8 M⊙) during the asymptotic giant branch (AGB) phase in the Spitzer two-colour and colour-magnitude diagrams. We follow the formation and growth of dust particles in the circumstellar envelope with an isotropically expanding wind, in which gas molecules impinge upon pre-existing seed nuclei, favour their growth. These models are the first able to identify the main regions in the Spitzer data occupied by AGB stars in the Large Magellanic Cloud (LMC). The main diagonal sequence traced by LMC extreme stars in the [3.6] - [4.5] versus [5.8] - [8.0] and [3.6] - [8.0] versus [8.0] planes is nicely fit by carbon stars models; it results to be an evolutionary sequence with the reddest objects being at the final stages of their AGB evolution. The most extreme stars, with [3.6] - [4.5] > 1.5 and [3.6] - [8.0] > 3, are 2.5-3 M⊙ stars surrounded by solid carbon grains. In higher mass (>3 M⊙) models dust formation is driven by the extent of hot bottom burning (HBB) - most of the dust formed is in the form of silicates and the maximum obscuration phase by dust particles occurs when the HBB experienced is strongest, before the mass of the envelope is considerably reduced.