  A promising source of the positrons that contribute through annihilation to
the diffuse Galactic 511keV emission is the beta-decay of unstable nuclei like
56Ni and 44Ti synthesised by massive stars and supernovae. Although a large
fraction of these positrons annihilate in the ejecta of SNe/SNRs, no
point-source of annihilation radiation appears in the INTEGRAL/SPI map of the
511keV emission. We exploit the absence of detectable annihilation emission
from young local SNe/SNRs to derive constraints on the transport of MeV
positrons inside SN/SNR ejecta and their escape into the CSM/ISM, both aspects
being crucial to the understanding of the observed Galactic 511keV emission. We
simulated 511keV lightcurves resulting from the annihilation of the decay
positrons of 56Ni and 44Ti in SNe/SNRs and their surroundings using a simple
model. We computed specific 511keV lightcurves for Cas A, Tycho, Kepler,
SN1006, G1.9+0.3 and SN1987A, and compared these to the upper-limits derived
from INTEGRAL/SPI observations. The predicted 511keV signals from positrons
annihilating in the ejecta are below the sensitivity of the SPI instrument by
several orders of magnitude, but the predicted 511keV signals for positrons
escaping the ejecta and annihilating in the surrounding medium allowed to
derive upper-limits on the positron escape fraction of ~13% for Cas A, ~12% for
Tycho, ~30% for Kepler and ~33% for SN1006. The transport of ~MeV positrons
inside SNe/SNRs cannot be constrained from current observations of the 511keV
emission from these objects, but the limits obtained on their escape fraction
are consistent with a nucleosynthesis origin of the positrons that give rise to
the diffuse Galactic 511keV emission.

High Energy Astrophysical Phenomena