Context. Transition disks have dust-depleted inner regions and may represent an intermediate step of an on-going disk dispersal process, where planet formation is probably in progress. Recent millimetre observations of transition disks reveal radially and azimuthally asymmetric structures, where micron- and millimetre-sized dust particles may not spatially coexist. These properties can be the result of particle trapping and grain growth in pressure bumps originating from the disk interaction with a planetary companion. The multiple features observed in some transition disks, such as SR 21, suggest the presence of more than one planet. Aims: We aim to study the gas and dust distributions of a disk hosting two massive planets as a function of different disk and dust parameters. Observational signatures, such as spectral energy distributions, sub-millimetre, and polarised images, are simulated for various parameters. Methods: Two dimensional hydrodynamical and one dimensional dust evolution numerical simulations are performed for a disk interacting with two massive planets. Adopting the previously determined dust distribution, and assuming an axisymmetric disk model, radiative transfer simulations are used to produce spectral energy distributions and synthetic images in polarised intensity at 1.6 µm and sub-millimetre wavelengths (850 µm). We analyse possible scenarios that can lead to gas azimuthal asymmetries. Results: We confirm that planets can lead to particle trapping, although for a disk with high viscosity (aturb = 10-2), the planet should be more massive than 5 MJup and dust fragmentation should occur with low efficiency (vf ~ 30 m s-1). This will lead to a ring-like feature as observed in transition disks in the millimetre. When trapping occurs, we find that a smooth distribution of micron-sized grains throughout the disk, sometimes observed in scattered light, can only happen if the combination of planet mass and turbulence is such that small grains are not fully filtered out. A high disk viscosity (aturb = 10-2) ensures a replenishment of the cavity in micron-sized dust, while for lower viscosity (aturb = 10-3), the planet mass is constrained to be less than 5 MJup. In these cases, the gas distribution is likely to show low-amplitude azimuthal asymmetries caused by disk eccentricity rather than by long-lived vortices.
