  Within the third quantisation formalism, we find solutions of the
Wheeler-DeWitt in terms of two sets of modes that can be identified with the
Hartle-Hawking's no boundary condition and with the Vilenkin's tunneling
boundary condition, respectively. The two sets of modes are related by a
Bogolyubov transformation so the no boundary vacuum state turns out to be
equivalent to a thermal distribution of tunnelling positive and negative modes
representing, in a relative sense, universes and antiuniverses
