We present a first combined analysis of the morphological and dynamical properties for the intermediate-mass Galaxy Evolution Sequence (IMAGES) sample. It is a representative sample of 52 z ∼ 0.6 galaxies with M stell from 1.5 to 15×10 10 M that possesses 3D resolved kinematics and HST deep imaging in at least two broad band filters. We aim at evaluating the evolution of rotating spirals robustly since z ∼ 0.6, as well as at testing the different schemes for classifying galaxies morphologically. We used all the information provided by multi-band images, color maps, and 2D light fitting to assign a morphological class to each object. We divided our sample into spiral disks, peculiar objects, compact objects, and mergers. Using our morphological classification scheme, 4/5 of the identified spirals are rotating disks, and more than 4/5 of identified peculiar galaxies show complex kinematics, while automatic classification methods such as concentration-asymmetry and GINI-M20 severely overestimate the fraction of relaxed disk galaxies. Using this methodology, we find that the fraction of undisturbed rotating spirals has increased by a factor ∼2 during the past 6 Gyr, a much higher fraction than was found previously based on morphologies alone. These rotating spiral disks are forming stars very rapidly, even doubling their stellar masses over the past 6 Gyr, while most of their stars were formed a few Gyr earlier, which reveals a large gas supply. Because they are the likely progenitors of local spirals, we can conjecture how their properties are evolving. Their disks show some evidence of inside-out growth, and the gas supply/accretion is not random since the disk needs to be stable in order to match the local disk properties.