agrep or tre-grep will do what you're asking; they're "approximate" regex matching/grep. For more information, also see the Wikipedia article.
% tre-agrep --help | head (05-23 16:53)
Usage: tre-agrep [OPTION]... PATTERN [FILE]...
Searches for approximate matches of PATTERN in each FILE or standard input.
Example: `tre-agrep -2 optimize foo.txt' outputs all lines in file `foo.txt' that
match "optimize" within two errors. E.g. lines which contain "optimise",
"optmise", and "opitmize" all match.
Regexp selection and interpretation:
-e, --regexp=PATTERN use PATTERN as a regular expression
-i, --ignore-case ignore case distinctions
-k, --literal PATTERN is a literal string
% agrep | head (05-23 16:53)
usage: agrep [-@#abcdehiklnoprstvwxyBDGIMSV] [-f patternfile] [-H dir] pattern [files]
summary of frequently used options:
(For a more detailed listing see 'man agrep'.)
-#: find matches with at most # errors
-c: output the number of matched records
-d: define record delimiter
-h: do not output file names
-i: case-insensitive search, e.g., 'a' = 'A'
-l: output the names of files that contain a match
-n: output record prefixed by record number
-v: output those records that have no matches
-w: pattern has to match as a word, e.g., 'win' will not match 'wind'
-B: best match mode. find the closest matches to the pattern
-G: output the files that contain a match
-H 'dir': the cast-dictionary is located in directory 'dir'