So many years ahead, I came back to answer this question.
To peek at the intermediate layers the best and easiest solution is to export the docker image into archived format and than every layer will be a tar on its own inside the bigger tar which is of the docker image.
Let's take for example docker image of tomcat:9.0
To export it into tar format:
docker save tomcat:9.0 >tomcat-9.0.tar
When exported, inside it there can be found many Layers , each one is archived in its own tar file:
tar -tvf tomcat-9.0.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 1fdef6bff31128d5a1a41bdd5fea06be032ef59fd985da09842a252310b4afa3/
-rw-r--r-- 0/0 3 2022-09-02 12:41 1fdef6bff31128d5a1a41bdd5fea06be032ef59fd985da09842a252310b4afa3/VERSION
-rw-r--r-- 0/0 482 2022-09-02 12:41 1fdef6bff31128d5a1a41bdd5fea06be032ef59fd985da09842a252310b4afa3/json
-rw-r--r-- 0/0 20891136 2022-09-02 12:41 1fdef6bff31128d5a1a41bdd5fea06be032ef59fd985da09842a252310b4afa3/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 2ecda9f325b8b38fc5e0a2f1fed4526c517c087e909875abdf1ee4fbcab37b30/
-rw-r--r-- 0/0 3 2022-09-02 12:41 2ecda9f325b8b38fc5e0a2f1fed4526c517c087e909875abdf1ee4fbcab37b30/VERSION
-rw-r--r-- 0/0 482 2022-09-02 12:41 2ecda9f325b8b38fc5e0a2f1fed4526c517c087e909875abdf1ee4fbcab37b30/json
-rw-r--r-- 0/0 329143808 2022-09-02 12:41 2ecda9f325b8b38fc5e0a2f1fed4526c517c087e909875abdf1ee4fbcab37b30/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 2fe9b9ee40730bab9cf86153dd37fbddb4990dd09ba5b9f22e55eeae13063fe8/
-rw-r--r-- 0/0 3 2022-09-02 12:41 2fe9b9ee40730bab9cf86153dd37fbddb4990dd09ba5b9f22e55eeae13063fe8/VERSION
-rw-r--r-- 0/0 406 2022-09-02 12:41 2fe9b9ee40730bab9cf86153dd37fbddb4990dd09ba5b9f22e55eeae13063fe8/json
-rw-r--r-- 0/0 80354304 2022-09-02 12:41 2fe9b9ee40730bab9cf86153dd37fbddb4990dd09ba5b9f22e55eeae13063fe8/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 3fff0862317ff87f1d757557325c158d405afd7fd98f31544ce10cf3ad2bdaa7/
-rw-r--r-- 0/0 3 2022-09-02 12:41 3fff0862317ff87f1d757557325c158d405afd7fd98f31544ce10cf3ad2bdaa7/VERSION
-rw-r--r-- 0/0 482 2022-09-02 12:41 3fff0862317ff87f1d757557325c158d405afd7fd98f31544ce10cf3ad2bdaa7/json
-rw-r--r-- 0/0 3072 2022-09-02 12:41 3fff0862317ff87f1d757557325c158d405afd7fd98f31544ce10cf3ad2bdaa7/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 5cab171b0d1115044b08690329f32a7d99a546777097e935733a837100ef34c5/
-rw-r--r-- 0/0 3 2022-09-02 12:41 5cab171b0d1115044b08690329f32a7d99a546777097e935733a837100ef34c5/VERSION
-rw-r--r-- 0/0 482 2022-09-02 12:41 5cab171b0d1115044b08690329f32a7d99a546777097e935733a837100ef34c5/json
-rw-r--r-- 0/0 3072 2022-09-02 12:41 5cab171b0d1115044b08690329f32a7d99a546777097e935733a837100ef34c5/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 6b87b21c947802c9f53a614692b4369cc2d7aa951f64bf28cd1f8713e191894e/
-rw-r--r-- 0/0 3 2022-09-02 12:41 6b87b21c947802c9f53a614692b4369cc2d7aa951f64bf28cd1f8713e191894e/VERSION
-rw-r--r-- 0/0 482 2022-09-02 12:41 6b87b21c947802c9f53a614692b4369cc2d7aa951f64bf28cd1f8713e191894e/json
-rw-r--r-- 0/0 50671616 2022-09-02 12:41 6b87b21c947802c9f53a614692b4369cc2d7aa951f64bf28cd1f8713e191894e/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 12:41 895adbb30677e7148af6d01e295347bd6ddc7cd5d929ee8fc3d03aedac5fa857/
-rw-r--r-- 0/0 3 2022-09-02 12:41 895adbb30677e7148af6d01e295347bd6ddc7cd5d929ee8fc3d03aedac5fa857/VERSION
-rw-r--r-- 0/0 2588 2022-09-02 12:41 895adbb30677e7148af6d01e295347bd6ddc7cd5d929ee8fc3d03aedac5fa857/json
-rw-r--r-- 0/0 2048 2022-09-02 12:41 895adbb30677e7148af6d01e295347bd6ddc7cd5d929ee8fc3d03aedac5fa857/layer.tar
-rw-r--r-- 0/0 12431 2022-09-02 12:41 d4488b7f8c9b73c0f2e91f5e37990905ae3d34d55ea893b5e70b76fc7a2db1b7.json
-rw-r--r-- 0/0 661 1970-01-01 01:00 manifest.json
-rw-r--r-- 0/0 86 1970-01-01 01:00 repositories
To see and peek at the content of each layer, all what is left now is to decompress the tomcat tar and than decompress the tar of the targeted layer.
tar -xvf tomcat-9.0.tar
tar -tvf 6b87b21c947802c9f53a614692b4369cc2d7aa951f64bf28cd1f8713e191894e/layer.tar
drwxr-xr-x 0/0 0 2022-09-02 07:24 etc/
drwxr-xr-x 0/0 0 2022-09-02 07:24 etc/ca-certificates/
-rwxr-xr-x 0/0 0 1970-01-01 01:00 etc/ca-certificates/.wh..wh..opq
drwxr-xr-x 0/0 0 2021-10-16 18:09 etc/ca-certificates/update.d/
-rw-r--r-- 0/0 5529 2022-09-02 07:24 etc/ca-certificates.conf
drwxr-xr-x 0/0 0 2022-09-02 07:24 etc/default/
-rw-r--r-- 0/0 35 2022-09-02 07:24 etc/default/locale
drwxr-xr-x 0/0 0 2022-09-02 07:24 etc/fonts/
-rwxr-xr-x 0/0 0 1970-01-01 01:00 etc/fonts/.wh..wh..opq
drwxr-xr-x 0/0 0 2022-09-02 07:24 etc/fonts/conf.avail/
[...]