  We prove boundedness results on modulation and Wiener amalgam spaces for some
families of spectral multipliers for the twisted Laplacian. We exploit the
metaplectic equivalence relating the twisted Laplacian with a partial harmonic
oscillator, leading to a general transference principle for the corresponding
spectral multipliers. Our analysis encompasses powers of the twisted Laplacian
and oscillating multipliers, with applications to the corresponding
Schr\"odinger and wave flows. On the other hand, elaborating on the twisted
convolution structure of the eigenprojections and its connection with the Weyl
product of symbols, we obtain a complete picture of the boundedness of the heat
flow for the twisted Laplacian. Results of the same kind are established for
fractional heat flows via subordination.
