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We present new observations of the merging system Arp 299 obtained with the IRAM Plateau de Bure interferometer. We have observed the ¹² CO(1-0), ¹² CO(2-1), ¹³ CO(1-0) and HCN(1-0) lines. For the ¹² CO(1-0) line, short spacings were recovered by using 30m data; about half of the total flux is found in weak and extended emission filtered out by the interferometer. The ¹² CO(1-0) map shows three bright regions associated with the nuclei of the galaxies (IC 694=A and NGC 3690=B) and to a star-forming region, C-C', which contains about one-third of the CO emission, but also extended emission and several ``filaments'' joining the bright regions. We find a south-east extension (A2) in IC 694 which corresponds to bright H<sub>2</sub> and Brγ emission. The <sup>12</sup> CO(2-1) map which has 0.7"x0.6" resolution but does not include short spacings shows the same gross features and is dominated by extremely bright emission in the nucleus of IC 694. Strong HCN emission is also observed in the nucleus of IC 694 (A), indicating the presence of large amounts of dense gas; weaker emission is found in B, C and C': the <sup>12</sup> CO/HCN ratio varies between 20 and 40 in the body of Arp 299, while it is about 7 in nucleus A. B is weak in <sup>13</sup> CO(1-0) emission, with a <sup>12</sup> CO/<sup>13</sup> CO ratio of about 30, while A and C-C' exhibit more ``normal'' ratios (11-16). Globally, C, C' and A2 exhibit line ratios that are typical of galactic disks, while A and B are clearly peculiar, with in particular HCN stronger than ¹³ CO. We find in the CO(1-0) line a regular velocity gradient over the south-east part of IC 694, which apparently extends to the C-C' region. The other regions of Arp 299 have more complex dynamics; from the high-resolution ¹² CO(2-1) maps, we are able to locate the dynamical center of NGC 3690 at the position of the radiocontinuum peak. We see clear indications that there is some gas flowing between IC 694 and NGC 3690. The three main regions are then dynamically and physically connected. In Arp 299, gas transfers have thus already occcured at an early stage of the merger.