  We present a local approach to the study of scale-to-scale energy transfers
in magnetohydrodynamic (MHD) turbulence. This approach is based on performing
local averages of the physical fields, which amounts to filtering scales
smaller than some parameter $\ell$. A key step in this work is the derivation
of a local K\'arm\'an-Howarth-Monin relation which provides a local form of
Politano and Pouquet's 4/3-law, without any assumption of homogeneity or
isotropy. Our approach is exact, non-random, and we show its connection to the
usual statistical results of turbulence. Its implementation on data obtained
via a three dimensional direct numerical simulation of the forced,
incompressible MHD equations from the John Hopkins turbulence database
constitutes the main part of our study. First, we show that the local
K\'arm\'an-Howarth-Monin relation holds well. The space statistics of local
cross-scale transfers is studied next, their means and standard deviations
being maximum at inertial scales, and their probability density functions
(PDFs) displaying very wide tails. Events constituting the tails of the PDFs
are shown to form structures of strong transfers, either positive or negative,
and which can be observed over the whole available range of scales. As $\ell$
is decreased, these structures become more and more localized in space while
contributing to an increasing fraction of the mean energy cascade rate.
Finally, we highlight their quasi 1D (filament-like) or quasi 2D
(sheet/ribbon-lke) nature, and show that they appear in areas of strong
vorticity or electric current density.
