  We introduce marked relative Pandharipande-Thomas (PT) invariants for a pair
$(X,D)$ of a smooth projective threefold and a smooth divisor. These invariants
are defined by integration over the moduli space of $r$-marked stable pairs on
$(X,D)$, and appear naturally when degenerating diagonal insertions via the
Li-Wu degeneration formula. We propose a Gromov-Witten (GW) / PT correspondence
for marked relative invariants. We show compatibility of the conjecture with
the degeneration formula and a splitting formula for relative diagonals. The
results provide new tools to prove GW/PT correspondences for varieties with
vanishing cohomology.
  As an application we prove the GW/PT correspondence for: (i) all Fano
complete intersections, and (ii) the reduced theories of $(S \times C, S \times
\{ z_1, \ldots, z_N \})$ where $S$ is a K3 surface and $C$ is a curve, for all
curve classes which have divisibility at most $2$ over the K3 surface.
  In the appendix we introduce a notion of higher-descendent invariants which
can be seen as an analogue of the nodal Gromov-Witten invariants defined by
Arg\"uz, Bousseau, Pandharipande and Zvonkine in \cite{ABPZ}. We show that the
higher-descendent invariants reduce to marked relative invariants with diagonal
insertions.
