  Cross-lingual transfer between a high-resource language and its dialects or
closely related language varieties should be facilitated by their similarity.
However, current approaches that operate in the embedding space do not take
surface similarity into account. This work presents a simple yet effective
strategy to imrove cross-lingual transfer between closely related varieties. We
propose to augment the data of the high-resource source language with
character-level noise to make the model more robust towards spelling
variations. Our strategy shows consistent improvements over several languages
and tasks: Zero-shot transfer of POS tagging and topic identification between
language varieties from the Finnic, West and North Germanic, and Western
Romance language branches. Our work provides evidence for the usefulness of
simple surface-level noise in improving transfer between language varieties.
