  Binary mass transfer is at the forefront of some of the most exciting puzzles
of modern astrophysics, including Type Ia supernovae, gamma-ray bursts, and the
formation of most observed exotic stellar populations. Typically, the evolution
is assumed to proceed in isolation, even in dense stellar environments such as
star clusters. In this paper, we test the validity of this assumption via the
analysis of a large grid of binary evolution models simulated with the SeBa
code. For every binary, we calculate analytically the mean time until another
single or binary star comes within the mean separation of the mass-transferring
binary, and compare this time-scale to the mean time for stable mass transfer
to occur. We then derive the probability for each respective binary to
experience a direct dynamical interruption. The resulting probability
distribution can be integrated to give an estimate for the fraction of binaries
undergoing mass transfer that are expected to be disrupted as a function of the
host cluster properties. We find that for lower-mass clusters ($\lesssim 10^4$
M$_{\odot}$), on the order of a few to a few tens of percent of binaries
undergoing mass-transfer are expected to be interrupted by an interloping
single, or more often binary, star, over the course of the cluster lifetime,
whereas in more massive globular clusters we expect $\ll$ 1% to be interrupted.
Furthermore, using numerical scattering experiments performed with the FEWBODY
code, we show that the probability of interruption increases if perturbative
fly-bys are considered as well, by a factor $\sim 2$.
