One of the methods is to use external storage to exchange data between repositories is git bundle. This way you only have single files for each transfer, not intermediate Git repositories.

git bundle create

One of the methods is to use external storage to exchange data between repositories is git bundle. This way you only have single files for each transfer, not intermediate Git repositories.

Each "git push" turns into creation of a file, "git fetch" fetches things from that file.

Demo session

Creating the first repository and doing the first "push"

gitbundletest$ mkdir repo1

gitbundletest$ cd repo1

repo1$ git init
Initialized empty Git repository in /tmp/gitbundletest/repo1/.git/
repo1$ echo 1 > 1 && git add 1 && git commit -m 1
[master (root-commit) c8b9ff9] 1
 1 file changed, 1 insertion(+)
 create mode 100644 1

repo1$ git bundle create /tmp/1.bundle master HEAD
Enumerating objects: 3, done.
Counting objects: 100% (3/3), done.
Writing objects: 100% (3/3), 384 bytes | 384.00 KiB/s, done.
Total 3 (delta 0), reused 0 (delta 0)

"cloning" to the second repository (i.e. the second computer):

gitbundletest$ git clone /tmp/1.bundle repo2
Cloning into 'repo2'...
Receiving objects: 100% (3/3), done.

gitbundletest$ cd repo2/

repo2$ cat 1
1

Doing some changes and "pushing" them to another bundle file:

repo2$ echo 2 > 1 && git add 1 && git commit -m 2
[master 250d387] 2
 1 file changed, 1 insertion(+), 1 deletion(-)

repo2$ git bundle create /tmp/2.bundle origin/master..master origin/HEAD..HEAD
Enumerating objects: 5, done.
Counting objects: 100% (5/5), done.
Writing objects: 100% (3/3), 415 bytes | 415.00 KiB/s, done.
Total 3 (delta 0), reused 0 (delta 0)

"pulling" changes to the first repository:

repo2$ cd ../repo1

repo1$ git pull /tmp/2.bundle 
Receiving objects: 100% (3/3), done.
From /tmp/2.bundle
 * branch            HEAD       -> FETCH_HEAD
Updating c8b9ff9..250d387
Fast-forward
 1 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

repo1$ cat 1
2

Unlike the first bundle, second one contains only partial Git history and is not directly clonable:

repo1$ cd ..

gitbundletest$ git clone /tmp/2.bundle repo3
Cloning into 'repo3'...
error: Repository lacks these prerequisite commits:
error: c8b9ff94942039469fa1937f6d38d85e0e39893a 
fatal: bad object 250d38747656401e15eca289a27024c61e63ed68
fatal: remote did not send all necessary objects

There is disadvantage in using bundles that you need to manually specify what range of commits each bundle should contain. Unlike git push, git bundle does not keep track what was in previous bundle, you need to manually adjust refs/remotes/origin/master or bundles would be bigger than it could be.