3D maps of the ISM can be used to locate not only IS clouds, but also IS bubbles between the clouds that are blown by stellar winds and supernovae. We compare our 3D maps of the IS dust to the ROSAT diffuse X-ray background maps. In the Plane, there is a good correspondence between the locations and extents of the mapped nearby cavities and the 0.25 keV background emission distribution, showing that most of these nearby cavities contribute to this soft X-ray emission. Assuming a constant dust to gas ratio and homogeneous 1MK hot gas filling the cavities, we modeled in a simple way the 0.25 keV surface brightness along the Galactic plane as seen from the Sun, taking into account the absorption by the mapped clouds. The data-model comparison favors the existence of hot gas in the Local Bubble (LB). The average mean pressure in the local cavities is found to be on the order of about 10,000 cm-3K, in agreement with previous studies. The model overestimates the emission from the huge cavities in the 3rd quadrant. Using CaII absorption data, we show that the dust to CaII ratio is very small in this region, implying the presence of a large quantity of lower temperature (non-X-ray emitting) ionized gas, explaining at least part of the discrepancy. In the meridian plane, the two main brightness enhancements coincide well with the chimneys connecting the LB to the halo. No nearby cavity is found towards the bright North Polar Spur (NPS) at high latitude. We searched in the maps for the source regions of the 0.75 keV enhancements in the 4th and 1st quadrants. Tunnels and cavities are found to coincide with the main bright areas, however no tunnel nor cavity is found to match the low-latitude, brightest part of the NPS. In addition, the comparison between the maps and published spectra do not favor the nearby cavities located within about 200pc as potential source regions for the NPS.
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