The Dirac operator on the semi-axis with a compactly supported potential is investigated. Let
(
k
n
)
n
≥
1
(k_n)_{n\geq 1}
be the sequence of its resonances, taken with multiplicities and ordered so that
|
k
n
|
|k_n|
do not decrease as
n
n
grows. It is proved that for any sequence
(
r
n
)
n
≥
1
∈
ℓ
1
(r_n)_{n\geq 1} \in \ell ^1
such that the points
k
n
+
r
n
k_n + r_n
remain in the lower half-plane for all
n
≥
1
n\geq 1
, the sequence
(
k
n
+
r
n
)
n
≥
1
(k_n + r_n)_{n\geq 1}
is also a sequence of resonances of a similar operator. Moreover, it is shown that the potential of the Dirac operator changes continuously under such perturbations.