Semiconductor heterostructures as quantum dots demonstrate discrete atom-like energy level structure based on several hundred of electron confinement states. In the case of double QD (DQD) or double QR (DQR), there is a single electron spectrum composed of a set of quasi-doublets. We study these specific spectrum properties with their relation to the electron tunneling in DQD (DCQR) when the wave function of electron localized initially in one of the double quantum object is spread into whole system. The double InAs/GaAs quantum dots are considered within the effective approach. Tunneling in DQD is studied in connection with change of inter-dot distance and QD geometry. There are two types of such tunneling in DQD. The first is related to tunneling in the system of two identical QDs; the second one occurs in the system of non-identical QDs. The tunneling in the DQR is a tunneling in the system with non-identical quantum objects. The quasi-doublets of the DQD spectrum play an important role in the tunneling. We study effect of violation of symmetry of DQD geometry on the tunneling and show that the violation of symmetry makes difficulties for such tunneling.