  The present paper is aimed to discussing three kinds of problems:
  (1) producing some ``mirror theorem'' for the recent mirror symmetric
construction, called \emph{framed} duality ($f$-duality), described in
\cite{R-fTV} and \cite{R-fpCI}: this is performed from the point of view
proposed by Homological Mirror Symmetry (HMS), by studying \emph{derived
equivalence} ($D$-equivalence) of multiple mirror models produced by means of
a, so-called, \emph{uncalibrated $f$-process}; (2) proposing a general
construction giving a big number of multiple mirror models to, in principle,
any projective complete intersection of non-negative Kodaira dimension: these
multiple mirrors turn out to be each other connected by means of uncalibrated
$f$-processes and then, after (1), $D$-equivalent or $K$-equivalent, in the
sense of Kawamata \cite{Kawamata}; (3) presenting a number of evidences for the
Bondal-Orlov-Kawamata conjecture that $D$-equivalence is $K$-equivalence, and
viceversa.

Algebraic Geometry