If your not using Google Webmaster Tools to track your backlinks, you won't know how many you really have, to a certain extent. When tracking Google backlinks using 3rd party software, most of the time none will be shown, and if they are show, its very minimal. The minimal amount that are shown, are considered by Google as having authority and relevancy to your website and to the internet itself. The more "AUTHORITY" backlinks you have, the higher your ranking. Simple!
If your backlinks come from good quality (good according to Google) sites then only Google lists them and better quality links take very less time to appear I have seen Google pick up links for my site in less the 4 days. Normally, it will take about 1-2 weeks to get the effect of your backlinks. However, if you can get backlinks from high traffic pages or sites, Google normally used to visit those sites very frequently. Google doesn't list every backlinks to your website, but yahoo does. That’s why you think yahoo is quicker. But I believe that Google is faster than Yahoo in indexing websites, so happened to me. If you links are listed in Yahoo, sure Google knows about them, but it may not list them. Use Social Bookmarking which all are high quality site according to Google also when you bookmark your website with Social Bookmarking site you will find most of them are authority site also so you will get very quick back link.
Google and yahoo are two different search engine and their methods and calculation back links is also different
I have over 200,000 backlinks on one of my websites, some PR6 and PR7, yet Google indexed 7 Backlinks total. All PR0-2 only. Therefore: Don't worry about Google Backlinks. Just because they don't show up, doesn't mean they aren't there.