I would say that saying you are interested in "various analyst postions" would get you nowhere in well over 90% of the companies. HR wants applications for specific jobs and they won't take the trouble to apply you to those jobs if you didn't take the trouble to apply.
Plus the actual qualifications for a financial analyst are considerably different than the qualifications for a database analyst which are different from the qualifications for a Business Analyst or a Security Systems Analyst or a Management Analyst. Analyst jobs are very different depending on the business they support and to say you want to apply for all of them indicates to any actual analyst (or manager of analysts) that you are most likely unqualified for any of them. Some analyst jobs require specific college degrees and others do not. Some require extensive business knowledge and some do not. Some require superficial statistical knowledge and some require a PhD in Statistics. I will point out that I have been both a management analyst and a data analyst and biggest similarity between the two was they had analyst in the name.
Now if you have a senior level manager contact who has reason outside of job qualifications to be interested in you (son of a customer or a niece who just graduated type of thing, not I just met you for five minutes at a conference) this approach might work for that specific company. But not really unless the manager is a C-level manager who can tell HR to consider you for all such positions.
If you are applying for multiple positions, then list each one specifically. Or write a separate cover letter for each application. What you are doing in saying "various analyst positions" looks as if you are not focused or worse not detail-oriented enough to bother looking at what was available which are bad traits for an analyst.
With over 30 years of analytical experience, I am pretty specific in what I expect from an analyst and generalizations (especially those to get you out of doing some extra work) don't show any analytical ability at all.
If you truly want an analytical job, you need to show those skills in your application. Different types of analyst jobs would need different discussions of why you are the best candidate in the cover letter and would require resumes that are different to emphasize different skills. A business analyst, for instance, needs business domain knowledge (what is needed for a business analyst in the pharmaceutical industry can be very different than what might be needed in the financial sector) and, most importantly, the ability to collect data from interviews with users and strong technical writing skills. A financial analyst may not have much direct people contact, but needs higher level accounting and mathematics skills and good report programming skills (which may include extensive knowledge of Excel and/or SQL). One cover letter and resume for both jobs would likely be weak for both because it would try to do too much.
