Hi Davit,
Thank you for reading that other thread. It immediately came to mind in reading your question, and when I see more than one report of mysterious ranking behavior, that's when I begin to wonder if Google has created some kind of new filter or is even experiencing a bug. The behavior that both you and the other poster are describing that is similar is that you rank well when searching from other parts of the country, but not from the business' own location. That's definitely mysterious, but the details of your business will tell us whether the scenarios are related or totally dissimilar..
Likely, you need to have a full audit done, Davit, and a forum can't replace investing in that, but let me take a quick gander here and tell you what I see:
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Searching from my location in NorCal for "car service to lax", I see you ranking 7th organically.
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You are not in the local pack for this search, and clicking through on the pack to the local finder, I am not finding you in the 3 tiers of results at the automatic zoom level. So, this counts as a pretty strong organic ranking but a strangely absent local ranking.
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I zoom in one level on the map. Google shows me two tiers of results and you are not there. I zoom in two levels, and you're still not there. I zoom in a third time and you are still not there, and Google is showing me irrelevant results like a UPS store and an auto parts store. On my 4th zoom, Google is showing me just two results, and they are irrelevant to my search - an automobile club and an auto parts store. So, what I've learned from this step is that your business does not appear to be suffering from the known earmarks of the Possum filter, which can result in filtered rankings at the automatic zoom level if two businesses are located near one another and share the same category. Rather, your business never appeared in the local finder no matter how many times I zoomed in.
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Next, I'm looking at your address in comparison to the address ranking #1 in the local pack. Google tells me that you are 23.6 miles away from your top competitor which is listed as LAX Town Car Service at 1 World Way, Los Angeles, CA 90045. You are 26.9 miles away from the #2 business, LAX Car Service -MGCLS located at 7828 Kittyhawk Ave, Los Angeles, CA 90045. And, you are 23.9 miles away from business #3, LA Confidential, at 101 World Way, Los Angeles, CA 90045. We've just learned that your business, located at 5322 Russell Ave #27, Los Angeles, CA 90027 is well over 20 miles away from the competitors Google is ranking in the local pack for me, as a distant searcher. You are not even in the same zip code as these three brands.
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Now, let's look up "los angeles" in Google and look at the map. You are 6.8 miles from Google’s centroid of the city which is located near City Hall at 200 N Spring St, Los Angeles, CA 90012. Your top competitor is even further away from City Hall, at a distance of 18.6 miles. So we are definitely seeing more an industry cluster than a city centroid cluster for your core search term. These are kind of old concepts, but sometimes I still find them to be applicable. You are within Google’s mapped boundaries of “los angeles” and are not in that cutout area they are making around Hollywood. So, city centroids and mapped borders are not excluding your from rankings, but significant distance from Google's industry cluster of businesses for your search term could be a factor.
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Exploring that last concept further, at the automatic zoom level for your search the furthest away Google is going for a listing for your search term is Flat Rate Car Service in West Hollywood at 8000 Sunset Blvd #45, Los Angeles, CA 90046. It is 12.1 miles from your top competitor on World Way. So, we see that, at least for my search from my location, Google is not setting a search radius that would include you in it, at 23.6 miles away from the top ranking business. From this, it’s reasonable to state that you may simply be too far away from Google’s 12 mile cluster of businesses for my search term. Good information.
7) However, all of the above being stated, the fact that you don’t come up at all no matter how many times I zoom in on the map is still sticking with me. If I am not able to see you in the local finder for my search at a great distance from your business and you are not able to see yourself in the local finder from your searches within LA, but you are ranking #7 organically, it’s at this point that I begin to become concerned that a local penalty of some kind could be at work. So, now, I want you to do something for me. I want you to search for this same term, “car service to lax” while standing inside of your place of business on Russel Ave. and verify for me that you are unable to find yourself AT ALL in the local pack. Then click through to the local finder and observe the results carefully, zooming in one level at a time, as I did in the above exercise. Tell me if you are not seeing yourself at all, even if you zoom in as many levels as Google allows you. Come back to me, please, and tell me what you see.

