  A numerical semigroup $M$ is a subset of the non-negative integers that is
closed under addition. A factorization of $n \in M$ is an expression of $n$ as
a sum of generators of $M$, and the Graver basis of $M$ is a collection
$Gr(M_t)$ of trades between the generators of $M$ that allows for efficient
movement between factorizations. Given positive integers $r_1, \ldots, r_k$,
consider the family $M_t = \langle t + r_1, \ldots, t + r_k\rangle$ of
"shifted" numerical semigroups whose generators are obtained by translating
$r_1, \ldots, r_k$ by an integer parameter $t$. In this paper, we characterize
the Graver basis $Gr(M_t)$ of $M_t$ for sufficiently large $t$ in the case $k =
3$, in the form of a recursive construction of $Gr(M_t)$ from that of smaller
values of $t$. As a consequence of our result, the number of trades in
$Gr(M_t)$, when viewed as a function of $t$, is eventually quasilinear. We also
obtain a sharp lower bound on the start of quasilinear behavior.
