  The ascent and descent of the Mittag-Leffler property were instrumental in
proving Zariski locality of the notion of an (infinite dimensional) vector
bundle by Raynaud and Gruson in \cite{RG}. More recently, relative
Mittag-Leffler modules were employed in the theory of (infinitely generated)
tilting modules and the associated quasi-coherent sheaves, \cite{AH},
\cite{HST}. Here, we study the ascent and descent along flat and faithfully
flat homomorphisms for relative versions of the Mittag-Leffler property. In
particular, we prove the Zariski locality of the notion of a locally
f-projective quasi-coherent sheaf for all schemes, and for each $n \geq 1$, of
the notion of an $n$-Drinfeld vector bundle for all locally noetherian schemes.
