Deep learning (DL) inversion of induction logging measurements is used in well geosteering for real-time imaging of the distribution of subsurface electrical conductivity. We develop a DL inversion workflow to solve 2.5-D inverse problems arising in well geosteering. The inversion workflow employs three DL modules: a 'look-around' fault detection module and two inversion modules for reconstructing anisotropic resistivity models in the presence or absence of fault planes, respectively. Our DL approach is capable of detecting and quantifying arbitrary dipping fault planes in real time. We compare inversion performance considering only short logging-while-drilling (LWD) measurements versus using both short LWD and deep-sensing measurements. The latter measurements provide enhanced depth-of-investigation while minimizing uncertainty. We also obtain improved results when using multidimensional inversion, especially nearby fault planes. This study verifies the applicability of real-time 2.5-D DL inversion across arbitrary faulted formations for well geosteering.