Let's say, we have a Calabi--Yau threefold $X$ (a three dimensional non-singular complex variety whose canonical bundle $K_X$ is trivial or equivalently a non-singular complex variety with a nowhere vanishing holomorphic $(3,0)$--form).
Question: For a different complex structure, can we still find a no-where vanishing $(3,0)$-form which makes $X$ a Calabi-Yau threefold? If so, why?
Note: I am trying to understand the existence of so-called "the vacuum line bundle" on the moduli space of complex structures of a Calabi-Yau threefold.